Transformation and summation formulas for Kampe de Feriet series.

Abstract

The double hypergeometric Kampé de Fériet series $F_{1:1}^{0:3}(1,1)$ depends upon 9 complex parameters. We present three cases with 2 relations between those 9 parameters, and show that under these circumstances $F_{1:1}^{0:3}(1,1)$ can be written as a ${}_4{F}_3(1)$ series. Some limiting cases of these transformation formulas give rise to new summation results for special $F_{1:1}^{0:3}(1,1)$'s. The actual transformation results arose out of the study of 9-$j$ coefficients.

Cited by in corpus (1)

• Multiple hypergeometric series -- Appell series and beyond