(j3.2006) Special math functions

Van Snyder van.snyder
Mon Apr 30 21:02:56 EDT 2007

On Thu, 2007-04-26 at 14:20 +0100, Fred J. Tydeman wrote:
> C and C++ have been working on adding special math functions.
> At this week's C standard's meeting, mention was made that
> the work will probably be turned into its own International 
> Standard.  Here is the C version of those functions:
> http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1182.pdf
> ---
> Fred J. Tydeman        Tydeman Consulting
> tydeman at tybor.com      Testing, numerics, programming
> +1 (775) 358-9748      Vice-chair of J11 (ANSI "C")
> Sample C99+FPCE tests: http://www.tybor.com
> Savers sleep well, investors eat well, spenders work forever.

In addition to wg14/n1182, I have been asked to provide software or
algorithms for the incomplete Gamma and Beta functions, inverses of both
w.r.t. each of their arguments, polygamma (at least psi) functions,
inverse error function, sine and cosine integrals, Fresnel integrals,
Dawson's function, Voigt's function, Heumann's lambda function,
spherical Bessel functions of the second kind, Airy functions, confluent
hypergeometric functions, parabolic cylinder functions, Mathieu
functions, Lam? (ellipsoidal harmonic) functions, Miejer G functions,
Kelvin functions, Lommel functions, Euler's dilogarithm, Jacobi and
Weierstrass elliptic functions, Struve functions, Anger-Weber functions,
various kinds of orthogonal polynomials (esp. Chebyshev, Gegenbauer and
Jacobi), Lerch zeta functions, Carlson's R functions, Bulirsch's cel
functions, pFq (as Bill remarked) which subsumes many of the others but
at sometimes substantial additional computational cost, ..., and I've
needed many of those in my own work.  Also the Fadeeva (aka plasma
dispersion) function, which is a complex function of complex argument
that subsumes several of the others.  So far, nobody has asked me for
Einstein's function, Debye's function or Bateman's function.

But... I don't see a need for an International Standard in this area.

Van Snyder                    |  What fraction of Americans believe 
Van.Snyder at jpl.nasa.gov       |  Wrestling is real and NASA is fake?
Any alleged opinions are my own and have not been approved or
disapproved by JPL, CalTech, NASA, the President, or anybody else.

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