Some reduction formulae for double power series and Kampé de Fériet functions

Abstract

Application of suitable 4 F 3[1] summation theorems leads to a number of formulae expressing certain double power series with equal variables as single power series. These formulae yield as particular cases reduction formulae expressing Kampé de Fériet functions F q:1:1 p:2:2 [ X, X] with certain parameter conditions in terms of either p+3 F q+2 [ X] or p+2 F q+1 [ X].