Expression of special stretched 9j coefficients in terms of 5F4 hypergeometric series

The Clebsch–Gordan coefficients or Wigner 3j symbols are known to be proportional to a 3F2(1) hypergeometric series, and Racah 6j coefficients to 4F3(1). In general, however, non-trivial 9j symbols cannot be expressed as 5F4. In this paper, we show, using the Dougall–Ramanujan identity, that special stretched 9j symbols can be reformulated as 5F4(1) hypergeometric series.