X-Nico

unusual facts about Special functions


Special functions

The later Bateman Manuscript Project, under the editorship of Arthur Erdélyi, attempted to be encyclopedic, and came around the time when electronic computation was coming to the fore and tabulation ceased to be the main issue.


Gal's accurate tables

Gal's accurate tables is a method devised by Shmuel Gal to provide accurate values of special functions using a lookup table and interpolation.

James A. Wilson

James Arthur Wilson is a mathematician working on special functions and orthogonal polynomials who introduced Wilson polynomials, Askey–Wilson polynomials and the Askey–Wilson beta integral.

Lists of integrals

An even larger, multivolume table is the Integrals and Series by Prudnikov, Brychkov, and Marichev (with volumes 1–3 listing integrals and series of elementary and special functions, volume 4–5 are tables of Laplace transforms).


see also

Arthur Erdélyi

Erdélyi was primarily an expert in special functions, in particular, Lamé functions, hypergeometric functions and orthogonal polynomials.

Francesco Tricomi

From 1943 to 1945 and from 1948 to 1951 at the California Institute of Technology of Pasadena, he collaborated on the manual of special functions for the Bateman manuscript project, together with Arthur Erdélyi, Wilhelm Magnus and Fritz Oberhettinger.

Uvea

In addition some uveal regions have special functions of great importance, including secretion of the aqueous humour by the ciliary processes, control of accommodation (focus) by the ciliary body, and optimisation of retinal illumination by the iris's control over the pupil.