Multiple hypergeometric functions and 9-j coefficients

Abstract

It is well known that the 9-j recoupling coefficient appearing in the quantum theory of angular momentum has 72 symmetries. However, the triple-sum series expression for the 9-j coefficient exhibits none of these symmetries. Here a stretched 9-j coefficient, for which a closed-form (single-term) expression exists, is considered and the type of summation theorems the triple-sum series reduces is investigated for any of the 72 symmetries. Apart from well known single-summation theorems for hypergeometric functions, this analysis gives rise to new summation theorems for double and triple hypergeometric functions.