Transformation and summation formulas for double hypergeometric series

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 F1:1;20:3;4(1,1) and F0:2;21:2;2(1,1). The transformation formulas relate such double series to a single hypergeometric series of 4F3(1) type. By specializing certain parameters, a list of new summation formulas for F0:2;21:2;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.