[om] Bad bugs in trig CD

[Bill Naylor]

On Wed, 5 Nov 2003, Richard Fateman wrote:

> Date: Wed, 05 Nov 2003 08:10:47 -0800
> From: Richard Fateman <fateman at cs.berkeley.edu>
> Reply-To: om at openmath.org
> To: om at openmath.org
> Subject: Re: [om] Bad bugs in trig CD
>
> I have not seen enough of the DLMF recently to know how it
> is going, (the only full chapter I saw was on the Airy functions)
> but how about this:
> figure out what exactly it is that you wish to refer to
> in A&S as a definition, and copy it into the CD. You could
> also say that you believe it to be consistent with the
> definition in A&S and DLMF, but you don't require people
> to then go find one of those references.  There are many
> (equivalent) definitions of sine, cosine, etc.  Pick one.
> e.g. sine (etc) could be infinite series, good for real or
> complex, and as these things go, fairly constructive.

I was looking at A&S chapter 4 last night, and realised there where many
different possible definitions of most of these objects. A&S pick one as
a definition and then count the others as properties (which is fair
enough!). If we were to follow A&S though, it would be nice to have FMPs
describing the defining relations. In the case of the inverse functions
all of the definitions are given by integrals, which impose conditions on
the paths of integrations, e.g.:

arcsin(z) = \int^z_0 \frac{dt}{(1-t^2)^{0.5}
The path of integration must not cross the real axis

There is no way in OpenMath to talk about paths of integration yet, (at
least not with the present set of CDs, though I did see one on some jp web
site, maybe that should be submitted: Nobuki Takayama, is that your CD?)

We could only right these FMPs if this sort of CD was to be accepted by
the OpenMath society.

Bill

> RJF
>
> PS, I find this vaguely amusing since the need to define
> what is meant by such functions was one of the points I raised
> at OM meeting 1 or 2, adjacent to some ISSAC meeting.
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