From: "Raymond E. Rogers" <rerogers@gte.net>
Newsgroups: sci.math.num-analysis
Subject: Re: asin(x+y) = ?
Date: Fri, 29 Jan 1999 13:26:22 -0500
Keywords: Addition formulas for elliptic functions

As I recall; all of the functions satisfying:
F(x+y)=P(F(x),F(y))   P a  polynomial
are Elliptic Functions or degenerate versions of them.
A chapter on Elliptic functions is in: 
Whittaker, E. T. and G. N. Watson,
     A Course in Modern Analysis (Fourth Edition)
     Cambridge Univ. Press (1927).
Old but really should be in every mathematical analyst's library.
Older books on Elliptic functions are at:
http://moa.cit.cornell.edu/dienst-data/cdl-math-browse.html
These are old but I find them enjoyable since they "lack" the level of
abstraction in modern mathematics :):)
If you want the names of particular books at Cornell, email me and I
will check when I get home.
Presumably there are modern books but I haven't noticed them.  
If you need it, I have a Linux script to download, bind, and print the
books.  The print function at Cornell through internet is broke.

Enjoy
Ray

Miroslav D Trajkovic wrote:
> 
> Hi,
> 
> We all know additive trigonometric formulas, i.e
> 
> sin(a+b) = sin(a)*cos(b) + sin(b)*cos(a)
> 
> Are there corresponding formulas for inverse trignometrical functions,
> such as
> 
> asin(x+y) = P(asin(x),asin(y)),
> 
> where P represents polynomial or rational function in asin(x), asin(y)?
> 
> Thanks,
> 
> Miroslav
> 
> --
> Miroslav Trajkovic      voice: (914) 945-6465
> Philips Research          fax: (914) 945-6375
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