Transformation and summation formulas for double hypergeometric series

Abstract

A number of new transformation formulas for double hypergeometric series are presented. The series appearing here are the so-called Kampé de Fériet functions of type F 1:1;2 0:3;4(1,1) and F 0:2;2 1:2;2(1,1). The transformation formulas relate such double series to a single hypergeometric series of 4 F 3(1) type. By specializing certain parameters, a list of new summation formulas for F 0:2;2 1:2;2(1,1) series is obtained. The origin of the results comes from studying symmetries of the 9- j coefficient appearing in quantum theory of angular momentum.