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February 2014 Hypergeometric functions where two arguments differ by an integer
Christopher S. Withers, Saralees Nadarajah
Braz. J. Probab. Stat. 28(1): 140-149 (February 2014). DOI: 10.1214/12-BJPS199

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.

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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

Information

Published: February 2014
First available in Project Euclid: 5 February 2014

zbMATH: 06291465
MathSciNet: MR3165433
Digital Object Identifier: 10.1214/12-BJPS199

Rights: Copyright © 2014 Brazilian Statistical Association

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Vol.28 • No. 1 • February 2014
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