## Brazilian Journal of Probability and Statistics

### Hypergeometric functions where two arguments differ by an integer

#### 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.

#### Article information

Source
Braz. J. Probab. Stat., Volume 28, Number 1 (2014), 140-149.

Dates
First available in Project Euclid: 5 February 2014

https://projecteuclid.org/euclid.bjps/1391611342

Digital Object Identifier
doi:10.1214/12-BJPS199

Mathematical Reviews number (MathSciNet)
MR3165433

Zentralblatt MATH identifier
06291465

#### Citation

Withers, Christopher S.; Nadarajah, Saralees. Hypergeometric functions where two arguments differ by an integer. Braz. J. Probab. Stat. 28 (2014), no. 1, 140--149. doi:10.1214/12-BJPS199. https://projecteuclid.org/euclid.bjps/1391611342

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