Expression of special stretched $9j$ coefficients in terms of $_5F_4$ hypergeometric series

TL;DR

This paper demonstrates that certain special stretched $9j$ coefficients can be expressed as $_5F_4(1)$ hypergeometric series using the Dougall-Ramanujan identity, extending known hypergeometric representations of angular momentum coefficients.

Contribution

It introduces a new representation of specific $9j$ symbols as $_5F_4$ series, expanding the mathematical tools for angular momentum coupling coefficients.

Findings

Special stretched $9j$ symbols can be expressed as $_5F_4$ hypergeometric series.

The Dougall-Ramanujan identity is used to derive this new representation.

This extends the known hypergeometric series representations of angular momentum coefficients.

Abstract

The Clebsch-Gordan coefficients or Wigner $3j$ symbols are known to be proportional to a $_3F_2(1)$ hypergeometric series, and Racah $6j$ coefficients to a $_4F_3(1)$. In general, however, non-trivial $9j$ symbols can not be expressed as a $_5F_4$. In this letter, we show, using the Dougall-Ramanujan identity, that special stretched $9j$ symbols can be reformulated as $_5F_4(1)$ hypergeometric series.