Expression of special stretched $9j$ coefficients in terms of ${}_5{F}_4$ hypergeometric series

The Clebsch-Gordan coefficients or Wigner $3j$ symbols are known to be proportional to a ${}_3{F}_2(1)$ hypergeometric series, and Racah $6j$ coefficients to a ${}_4{F}_3(1)$. In general, however, non-trivial $9j$ symbols can not be expressed as a ${}_5{F}_4$. In this letter, we show, using the Dougall-Ramanujan identity, that special stretched $9j$ symbols can be reformulated as ${}_5{F}_4(1)$ hypergeometric series.