A generalised Kummer-type transformation for the pFp(x) hypergeometric function

A. R. Miller, Richard B. Paris

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function pFp(x) when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to p=1.
Original languageEnglish
Pages (from-to)571-578
Number of pages8
JournalCanadian Mathematical Bulletin
Volume55
DOIs
Publication statusPublished - 2012

Fingerprint

Hypergeometric Functions
Reduction formula
Confluent Hypergeometric Function
Generalized Hypergeometric Function
Alternatives

Cite this

@article{4886b6e483764477934d4ef0b66e4c01,
title = "A generalised Kummer-type transformation for the pFp(x) hypergeometric function",
abstract = "In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function pFp(x) when pairs of parameters differ by unity, by means of a reduction formula for a certain Kamp{\'e} de F{\'e}riet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to p=1.",
author = "Miller, {A. R.} and Paris, {Richard B.}",
year = "2012",
doi = "10.4153/CMB-2011-095-6",
language = "English",
volume = "55",
pages = "571--578",
journal = "Canadian Mathematical Bulletin",
issn = "0008-4395",
publisher = "Canadian Mathematical Society",

}

A generalised Kummer-type transformation for the pFp(x) hypergeometric function. / Miller, A. R.; Paris, Richard B.

In: Canadian Mathematical Bulletin, Vol. 55, 2012, p. 571-578.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A generalised Kummer-type transformation for the pFp(x) hypergeometric function

AU - Miller, A. R.

AU - Paris, Richard B.

PY - 2012

Y1 - 2012

N2 - In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function pFp(x) when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to p=1.

AB - In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function pFp(x) when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to p=1.

U2 - 10.4153/CMB-2011-095-6

DO - 10.4153/CMB-2011-095-6

M3 - Article

VL - 55

SP - 571

EP - 578

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

SN - 0008-4395

ER -