Abstract
If $\alpha_{1}-\beta_{1}$ is an integer, then ${}_{p}F_{q}(\boldsymbol{\alpha} ;\boldsymbol{\beta} :z)$ can be expressed in terms of ${}_{p-1}F_{q-1}$. This leads to a conjectured generalization of Kummer’s transformation from ${}_{1}F_{1}$ to ${}_{p}F_{q}$. Applications are given for noncentral chi-square and Student’s $t$ distributions.
Citation
Christopher S. Withers. Saralees Nadarajah. "Hypergeometric functions where two arguments differ by an integer." Braz. J. Probab. Stat. 28 (1) 140 - 149, February 2014. https://doi.org/10.1214/12-BJPS199
