[om] Specfun CD's (was: library)
Bruce Miller
bruce.miller at nist.gov
Tue Jun 19 16:18:27 CEST 2001
Mike Dewar wrote:
> Maybe the people involved could send snapshots of their current CDs to
> the list. I could also put them on the website and, provided that they
> conform to the standard, run them through David's XSL stylesheet so that
> they are a bit more readable.
I hope the list is quiet enough that dumping cd's here wont offend
anyone.
And I'd hate for the subject to die off.
So, here's the current draft of my specfun cd. As I said before,
it is minimal: It lists quite a few symbols and points to their
`definitions' in Abramowitz & Stegun. However, there are no
examples, etc.
BTW: Is this a general enough OM topic, or should it be taken off-line
(& if so, to who?)
----------------
Bruce Miller
<bruce.miller at nist.gov> http://math.nist.gov/~BMiller/
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<CD>
<CDName> specfun </CDName>
<CDURL> http://dlmf.nist.gov/om/cd/specfun.ocd </CDURL>
<CDReviewDate> ? </CDReviewDate>
<CDDate> 2001-03-12 </CDDate>
<CDVersion> 0 </CDVersion>
<CDRevision> 0 </CDRevision>
<CDStatus> experimental </CDStatus>
<CDUses>
<CDName>alg1</CDName>
<CDName>arith1</CDName>
<CDName>interval1</CDName>
<CDName>logic1</CDName>
<CDName>nums1</CDName>
<CDName>quant1</CDName>
<CDName>relation1</CDName>
<CDName>set1</CDName>
<CDName>setname1</CDName>
<CDName>complex1</CDName>
<CDName>transc1</CDName>
</CDUses>
<Description>
This CD holds the definitions of many special functions.
They are defined as in Abramovitz and Stegun, Handbook of Mathematical Functions.
</Description>
<CDDefinition>
<Name>ExpInt</Name>
<Description>
This symbol represents the exponential integral, E_1.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ExpInti</Name>
<Description>
This symbol represents the exponential integral, Ei.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.1.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>LogInt</Name>
<Description>
This symbol represents the exponential integral, li.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.1.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ExpIntn</Name>
<Description>
This symbol represents the exponential integral, E_n.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.1.4.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ExpIntAlpha</Name>
<Description>
This symbol represents the exponential integral, alpha.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.1.5.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ExpIntBeta</Name>
<Description>
This symbol represents the exponential integral, beta.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.1.6.
</Description>
</CDDefinition>
<CDDefinition>
<Name>SinInt</Name>
<Description>
This symbol represents the Sine integral, Si.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.2.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>CosInt</Name>
<Description>
This symbol represents the Cosine integral, Ci.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.2.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>SinhInt</Name>
<Description>
This symbol represents the hyperbolic Sine integral, Shi.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.2.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>CoshInt</Name>
<Description>
This symbol represents the hyperbolic Cosine integral, Chi.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.2.4.
</Description>
</CDDefinition>
<CDDefinition>
<Name>sinInt</Name>
<Description>
This symbol represents the sine integral, si (shifted).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 5.2.5.
</Description>
</CDDefinition>
<CDDefinition>
<Name>EulerGamma</Name>
<Description>
This symbol represents Euler's Gamma function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>EulerBeta</Name>
<Description>
This symbol represents Euler's Beta function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.2.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>digamma</Name>
<Description>
This symbol represents the Digamma (or psi) function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>GammaP</Name>
<Description>
This symbol represents the incomplete gamma function, P?.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.5.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>incgamma</Name>
<Description>
This symbol represents the incomplete gamma function, gamma.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.5.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>IncGamma</Name>
<Description>
This symbol represents the incomplete gamma function, Gamma.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.5.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>incgammastar</Name>
<Description>
This symbol represents the non-singular incomplete gamma function, gamma^*.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.5.4.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Pchi</Name>
<Description>
This symbol represents the probability integral of the $\chi^2$ distribution.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.5.5.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Pearsonsgamma</Name>
<Description>
This symbol represents Pearson's form of incomplete gamma function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.5.6.
</Description>
</CDDefinition>
<CDDefinition>
<Name>IncGammaC</Name>
<Description>
This symbol represents the incomplete cosine gamma function, C.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.5.7.
</Description>
</CDDefinition>
<CDDefinition>
<Name>IncGammaS</Name>
<Description>
This symbol represents the incomplete sine gamma function, S.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.5.8.
</Description>
</CDDefinition>
<CDDefinition>
<Name>IncBeta</Name>
<Description>
This symbol represents the incomplete Beta function, B.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.6.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>IncI</Name>
<Description>
This symbol represents the incomplete Beta function, I.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 6.6.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>erf</Name>
<Description>
This symbol represents the error function, erf.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>erfc</Name>
<Description>
This symbol represents the complementary error function, erfc.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.1.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>erfw</Name>
<Description>
This symbol represents the error function, w.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.1.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>FresnelCos</Name>
<Description>
This symbol represents the Fresnel cosine integral.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>FresnelSin</Name>
<Description>
This symbol represents the Fresnel sine integral.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.3.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>FresnelCosone</Name>
<Description>
This symbol represents the Fresnel cosine Integral (alternate 1).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>FresnelCostwo</Name>
<Description>
This symbol represents the Fresnel cosine integral (alternate 2).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>FresnelSinone</Name>
<Description>
This symbol represents the Fresnel sine integral (alternate 1).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.3.4.
</Description>
</CDDefinition>
<CDDefinition>
<Name>FresnelSintwo</Name>
<Description>
This symbol represents the Fresnel sine integral (alternate 2).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>DawsonsInt</Name>
<Description>
This symbol represents Dawson's Integral.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.x.x.
</Description>
</CDDefinition>
<CDDefinition>
<Name>VoigtU</Name>
<Description>
This symbol represents Voigt's U Function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.x.x.
</Description>
</CDDefinition>
<CDDefinition>
<Name>VoigtV</Name>
<Description>
This symbol represents Voigt's V Function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.x.x.
</Description>
</CDDefinition>
<CDDefinition>
<Name>RepInterfc</Name>
<Description>
This symbol represents the repeated integral of erfc.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 7.x.x.
</Description>
</CDDefinition>
<CDDefinition>
<Name>LegendreP</Name>
<Description>
This symbol represents the Legendre function of the first kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 8.1.2,8.4.1.
or 8.4.3, 8.4.5; or 8.6.18 (Rodrigues); or 8.12.1-3 (Conical)
</Description>
</CDDefinition>
<CDDefinition>
<Name>LegendreQ</Name>
<Description>
This symbol represents the Legendre function of the second kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 8.1.3,8.4.2.
or 8.4.4, 8.4.6; or 8.6.19 (Rodrigues); or 8.12.4 (Conical)
</Description>
</CDDefinition>
<CDDefinition>
<Name>FerrersP</Name>
<Description>
This symbol represents Ferrers' Legendre function of the first kind defined on -1<x<1.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 8.x.x.
</Description>
</CDDefinition>
<CDDefinition>
<Name>FerrersQ</Name>
<Description>
This symbol represents Ferrers' Legendre function of the second kind defined on -1<x<1.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 8.x.x.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselJ</Name>
<Description>
This symbol represents the Bessel function of the first kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselY</Name>
<Description>
This symbol represents the Bessel function of the second kind (Weber's function).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselH</Name>
<Description>
This symbol represents the Bessel function of the third kind (Hankel functions).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.1.1.
index i=1,2
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselModM</Name>
<Description>
This symbol represents the modulus of Bessel function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.2.17.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselTheta</Name>
<Description>
This symbol represents the phase of Bessel function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.2.17.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselModN</Name>
<Description>
This symbol represents the modulus of derivatives of Bessel functions.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.2.18.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselPhi</Name>
<Description>
This symbol represents the phase of derivatives of Bessel functions.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.2.18.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselI</Name>
<Description>
This symbol represents the modified Bessel function of the first kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.6.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BesselK</Name>
<Description>
This symbol represents the modified Bessel function of the second kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.6.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Cylinder</Name>
<Description>
This symbol represents a Cylinder function (linear combination of Bessel functions).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.x.x.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ModCylinder</Name>
<Description>
This symbol represents a modified Cylinder function (linear combination of modified Bessel functions).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.x.x.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Kelvinber</Name>
<Description>
This symbol represents the Kelvin function, ber.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.9.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Kelvinbei</Name>
<Description>
This symbol represents the Kelvin function, bei.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.9.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Kelvinker</Name>
<Description>
This symbol represents the Kelvin function, ker.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.9.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Kelvinkei</Name>
<Description>
This symbol represents the Kelvin function, kei.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 9.9.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>SphBesselJ</Name>
<Description>
This symbol represents the spherical Bessel function of the first kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>SphBesselY</Name>
<Description>
This symbol represents the spherical Bessel function of the second kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>SphBesselH</Name>
<Description>
This symbol represents the spherical Bessel function of the third kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.1.1.
index i=1,2
</Description>
</CDDefinition>
<CDDefinition>
<Name>SphBesselI</Name>
<Description>
This symbol represents the modified spherical Bessel function of first kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.2.2,10.2.3.
replaces confusing notation!
</Description>
</CDDefinition>
<CDDefinition>
<Name>SphBesselK</Name>
<Description>
This symbol represents the modified spherical Bessel function of third kind(?).
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.2.4.
replaces confusing notation!
</Description>
</CDDefinition>
<CDDefinition>
<Name>AiryAi</Name>
<Description>
This symbol represents the Airy function, Ai.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.4.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>AiryBi</Name>
<Description>
This symbol represents the Airy function, Bi.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.4.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ScorerGi</Name>
<Description>
This symbol represents the Scorer function, Gi.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.4.42.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ScorerHi</Name>
<Description>
This symbol represents the Scorer function, Hi.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 10.4.44.
</Description>
</CDDefinition>
<CDDefinition>
<Name>StruveH</Name>
<Description>
This symbol represents the Struve function, H.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 12.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>StruveL</Name>
<Description>
This symbol represents the modified Struve function, L.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 12.2.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>AngerJ</Name>
<Description>
This symbol represents Anger's function, J.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 12.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>WeberE</Name>
<Description>
This symbol represents Weber's function, E.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 12.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>KummerM</Name>
<Description>
This symbol represents Kummer's confluent hypergeometric function, M.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 13.1.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>KummerU</Name>
<Description>
This symbol represents Kummer's confluent hypergeometric Function, U.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 13.1.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>WhitM</Name>
<Description>
This symbol represents Whittaker's confluent hypergeometric function, M.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 13.1.32.
</Description>
</CDDefinition>
<CDDefinition>
<Name>WhitW</Name>
<Description>
This symbol represents Whittaker's confluent hypergeometric function, W.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 13.1.33-34.
</Description>
</CDDefinition>
<CDDefinition>
<Name>CoulombF</Name>
<Description>
This symbol represents the regular Coulomb wave function, F.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 14.1.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>CoulombG</Name>
<Description>
This symbol represents the irregular Coulomb wave function, G.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 14.1.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>HypergeoF</Name>
<Description>
This symbol represents Gauss's hypergeometric function, F.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 15.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>HyperpFq</Name>
<Description>
This symbol represents Gauss's Hypergeometric Function, pFq.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation Ch.~15.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobisn</Name>
<Description>
This symbol represents Jacobi's elliptic function, sn.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.1.5.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobicn</Name>
<Description>
This symbol represents Jacobi's elliptic function, cn.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.1.5.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobidn</Name>
<Description>
This symbol represents Jacobi's elliptic function, dn.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.1.5.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobicd</Name>
<Description>
This symbol represents Jacobi's elliptic function, cd.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobidc</Name>
<Description>
This symbol represents Jacobi's elliptic function, dc.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobins</Name>
<Description>
This symbol represents Jacobi's elliptic function, ns.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobisd</Name>
<Description>
This symbol represents Jacobi's elliptic function, sd.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobinc</Name>
<Description>
This symbol represents Jacobi's elliptic function, nc.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobids</Name>
<Description>
This symbol represents Jacobi's elliptic function, ds.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobind</Name>
<Description>
This symbol represents Jacobi's elliptic function, nd.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobisc</Name>
<Description>
This symbol represents Jacobi's elliptic function, sc.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Jacobics</Name>
<Description>
This symbol represents Jacobi's elliptic function, cs.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>JacobiTheta</Name>
<Description>
This symbol represents Jacobi Theta functions, Theta_i.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 16.27.1-4.
The index i is in \{1,2,3,4\}
</Description>
</CDDefinition>
<CDDefinition>
<Name>EllIntF</Name>
<Description>
This symbol represents the elliptic integral of the first kind, F.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 17.2.6.
</Description>
</CDDefinition>
<CDDefinition>
<Name>EllIntE</Name>
<Description>
This symbol represents the elliptic integral of the second kind, E.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 17.2.8.
</Description>
</CDDefinition>
<CDDefinition>
<Name>EllIntPi</Name>
<Description>
This symbol represents the elliptic integral of the third kind, Pi.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 17.2.14-16.
</Description>
</CDDefinition>
<CDDefinition>
<Name>CompEllIntK</Name>
<Description>
This symbol represents the complete elliptic integral of the first kind, F.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 17.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>CompEllIntE</Name>
<Description>
This symbol represents the complete elliptic integral of the second kind, E.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 17.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>EllipticNome</Name>
<Description>
This symbol represents the nome, q.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 17.3.17.
</Description>
</CDDefinition>
<CDDefinition>
<Name>JacobiZeta</Name>
<Description>
This symbol represents Jacobi's Zeta function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 17.3.27-28.
</Description>
</CDDefinition>
<CDDefinition>
<Name>HeumanLambda</Name>
<Description>
This symbol represents Heuman's Lambda function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 17.4.39.
</Description>
</CDDefinition>
<CDDefinition>
<Name>WeierP</Name>
<Description>
This symbol represents Weierstrass' P function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation Ch.~18.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Weierzeta</Name>
<Description>
This symbol represents Weierstrass' zeta function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation Ch.~18.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Weiersigma</Name>
<Description>
This symbol represents Weierstrass' sigma function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation Ch.~18.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Weierg</Name>
<Description>
This symbol represents the Weierstrass Invariants, g_i.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 18.1.1.
index i is 2 or 3
</Description>
</CDDefinition>
<CDDefinition>
<Name>Weiere</Name>
<Description>
This symbol represents Weierstrass ?.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 18.1.7.
index i is 1,2 or 3
</Description>
</CDDefinition>
<CDDefinition>
<Name>WeierH</Name>
<Description>
This symbol represents Weierstrass ?.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 18.3.5.
index i is 1,2 or 3
</Description>
</CDDefinition>
<CDDefinition>
<Name>WeierNome</Name>
<Description>
This symbol represents Weierstrass' nome.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 18.10.2.
Slightly different defn
</Description>
</CDDefinition>
<CDDefinition>
<Name>Weierm</Name>
<Description>
This symbol represents Weierstrass ?.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 18.9.9.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Parabolicy</Name>
<Description>
This symbol represents the parabolic cylinder function, y.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 19.2.1-4.
i = 1,2
</Description>
</CDDefinition>
<CDDefinition>
<Name>WhitU</Name>
<Description>
This symbol represents the Whittaker function, U.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 19.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>WhitV</Name>
<Description>
This symbol represents the Whittaker function, V.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 19.3.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>WhitD</Name>
<Description>
This symbol represents the Whittaker function, D.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation Ch.~19.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ParabolicW</Name>
<Description>
This symbol represents the parabolic function, W.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 19.17.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ParabolicE</Name>
<Description>
This symbol represents the parabolic function, E.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 19.17.6.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ParabolicEs</Name>
<Description>
This symbol represents the parabolic function, E^*.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 19.17.7.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Mathieuce</Name>
<Description>
This symbol represents the even Mathieu functions, ce.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation Ch.~20.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Mathieuse</Name>
<Description>
This symbol represents the odd Mathieu functions, se.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation Ch.~20.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MathieuCe</Name>
<Description>
This symbol represents the even Mathieu functions, Ce.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 20.6.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MathieuSe</Name>
<Description>
This symbol represents the odd Mathieu functions, Se.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 20.6.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MathieuMc</Name>
<Description>
This symbol represents the even Mathieu-Hankel functions, Mc.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 20.6.7-8.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MathieuMs</Name>
<Description>
This symbol represents the odd Mathieu-Hankel functions, Ms.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 20.6.9-10.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MathieuIe</Name>
<Description>
This symbol represents the Mathieu function, Ie.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 20.8.8.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MathieuIo</Name>
<Description>
This symbol represents the Mathieu function, Io.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 20.8.8.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MathieuKe</Name>
<Description>
This symbol represents the Mathieu function, Ke.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 20.8.9.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MathieuKo</Name>
<Description>
This symbol represents the Mathieu function, Ko.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 20.8.9.
</Description>
</CDDefinition>
<CDDefinition>
<Name>SpheroidalS</Name>
<Description>
This symbol represents the angular spheroidal wave function, S.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 21.6.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>SpheroidalR</Name>
<Description>
This symbol represents the radial spheroidal wave function, R.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 21.6.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ProlateS</Name>
<Description>
This symbol represents the prolate angular spheroidal wave function, S.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 21.7.1-2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>JacobiP</Name>
<Description>
This symbol represents the Jacobi polynomial, P.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>JacobiG</Name>
<Description>
This symbol represents the Jacobi polynomial, G.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Ultraspherical</Name>
<Description>
This symbol represents the ultraspherical (Gegenbauer) polynomial, C.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ChebyT</Name>
<Description>
This symbol represents the Chebyshev polynomial of the first kind, T.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.4.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ChebyU</Name>
<Description>
This symbol represents the Chebyshev polynomial of the second kind, U.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.5.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ChebyS</Name>
<Description>
This symbol represents the Chebyshev polynomial of the first kind, S.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.6.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ChebyC</Name>
<Description>
This symbol represents the Chebyshev polynomial of the second kind, C.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.7.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ChebyTs</Name>
<Description>
This symbol represents the shifted Chebyshev polynomial of the first kind, T^*.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.8.
</Description>
</CDDefinition>
<CDDefinition>
<Name>ChebyUs</Name>
<Description>
This symbol represents the shifted Chebyshev polynomial of the second kind, U^*.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.9.
</Description>
</CDDefinition>
<CDDefinition>
<Name>LegendrePoly</Name>
<Description>
This symbol represents the Legendre polynomial (spherical), P.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.10.
</Description>
</CDDefinition>
<CDDefinition>
<Name>LegendrePolys</Name>
<Description>
This symbol represents the shifted Legendre polynomial (spherical), P^*.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.11.
</Description>
</CDDefinition>
<CDDefinition>
<Name>LaguerreL</Name>
<Description>
This symbol represents the generalized Laguerre polynomial, L.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.12-13.
</Description>
</CDDefinition>
<CDDefinition>
<Name>HermiteH</Name>
<Description>
This symbol represents the Hermite polynomial, H.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.14.
</Description>
</CDDefinition>
<CDDefinition>
<Name>HermiteHe</Name>
<Description>
This symbol represents the Hermite polynomial He.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 22.2.15.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BernoulliB</Name>
<Description>
This symbol represents the Bernoulli polynomial, B.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 23.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>EulerE</Name>
<Description>
This symbol represents the Euler polynomial, E.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 23.1.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>RiemannZeta</Name>
<Description>
This symbol represents the Riemann zeta function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 23.2.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>StirlingS</Name>
<Description>
This symbol represents the Stirling numbers of First kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 24.1.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>StirlingSS</Name>
<Description>
This symbol represents the Stirling numbers of second kind.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 24.1.4.
</Description>
</CDDefinition>
<CDDefinition>
<Name>MoebiusMu</Name>
<Description>
This symbol represents the M\"obius Function, mu.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 24.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>EulerTotientPhi</Name>
<Description>
This symbol represents the Euler totient function, phi.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 24.3.2.
</Description>
</CDDefinition>
<CDDefinition>
<Name>DivisorSigma</Name>
<Description>
This symbol represents the divisor function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 24.3.3.
</Description>
</CDDefinition>
<CDDefinition>
<Name>GaussianProb</Name>
<Description>
This symbol represents the Gaussian probability function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 26.2.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>BivariateProb</Name>
<Description>
This symbol represents the bivariate probability function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 26.3.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>FVariance</Name>
<Description>
This symbol represents the F-Variance distribution function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 26.6.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>tDistribution</Name>
<Description>
This symbol represents the students t distribution function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 26.7.1.
</Description>
</CDDefinition>
<CDDefinition>
<Name>Debye</Name>
<Description>
This symbol represents the Debye functions.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 27.1.
What notation?
</Description>
</CDDefinition>
<CDDefinition>
<Name>Planck</Name>
<Description>
This symbol represents Planck's radiation function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 27.2.
What notation?
</Description>
</CDDefinition>
<CDDefinition>
<Name>Einstein</Name>
<Description>
This symbol represents the Einstein function.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 27.3.
What notation?
</Description>
</CDDefinition>
<CDDefinition>
<Name>SievertInt</Name>
<Description>
This symbol represents the Sievert integral.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 27.4.
What notation?
</Description>
</CDDefinition>
<CDDefinition>
<Name>Othera</Name>
<Description>
This symbol represents ?.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 27.5.
What name and notation?
</Description>
</CDDefinition>
<CDDefinition>
<Name>Otherb</Name>
<Description>
This symbol represents ?.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 27.6.
What name and notation?
</Description>
</CDDefinition>
<CDDefinition>
<Name>Dilogarithm</Name>
<Description>
This symbol represents the Dilogarithm.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 27.7.
What notation?
</Description>
</CDDefinition>
<CDDefinition>
<Name>ClausenInt</Name>
<Description>
This symbol represents Clausen's integral.
The function is defined in Abramovitz and Stegun, Handbook of Mathematical Functions,
equation 27.8.
</Description>
</CDDefinition>
</CD>
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