REPRESENTATION OF THE RACAH COEFFICIENT AS A GENERALIZED HYPERGEOMETRIC FUNCTION

Abstract

Publisher Summary It is possible to obtain an equivalent set of four series representations. Observations on the symmetries of the Racah coefficient are made in terms of these. The chapter presents a rearrangement of these four series repreentations into a new set of four and discusses their domains of validity. The chapter further explains the derivation of the binomial expansions for the Racah coefficient and discusses the connection between the two equivalent sets of 4 F 3 (1)s and the twelve binomial expansions, through the number of terms in a Racah coeeficient. Any one of the 4 F 3 (1)s belonging to set II accounts for only 36 of the known 144 symmetries of the Racah coefficient. The methods adopted for rearranging the single sum series of Racah to arrive at the binomial expansions or sets of 4 F 3 (1)s are different.