Transformation and summation formulas for Kampe de Feriet series.
Abstract
The double hypergeometric Kamp\'e de F\'eriet series F0:31:1(1,1) depends upon 9 complex parameters. We present three cases with 2 relations between those 9 parameters, and show that under these circumstances F0:31:1(1,1) can be written as a 4F3(1) series. Some limiting cases of these transformation formulas give rise to new summation results for special F0:31:1(1,1)'s. The actual transformation results arose out of the study of 9-j coefficients.
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