Some formulae for double Clausenian functions. (English) Zbl 0953.33010

Karlsson, Per W.

J. Comput. Appl. Math. 118, No. 1-2, 203-213 (2000).

The author derives reduction and transformation formulae for certain Kampé de Fériet functions from an Euler integral representation. A simple example case is given by formula (13): \[ F^{1:2;2}_{2:0;0}\left[\begin{matrix} a &b,&c &b',&c'\\ b+b',&c+c'& -;& -\end{matrix}\Bigl|x,{x\over x-1}\right]={_2F_1}\left[\begin{matrix} a,&b \\ b+b'\end{matrix}\Bigr|x\right]{_2F_1}\left[\begin{matrix} a,&c'\\ c+c'\end{matrix}\Bigl|{x \over x-1}\right].\Bigr. \]

Reviewer: Wolfram Koepf (Kassel)

MSC:

33C70

Other hypergeometric functions and integrals in several variables

Keywords:

Euler integrals; Kampé de Fériet functions; reduction formulae

References:

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