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

A. R. Miller; Richard B. Paris

doi:10.4153/CMB-2011-095-6

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

A. R. Miller, Richard B. Paris

Research output: Contribution to journal › Article › peer-review

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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 language	English
Pages (from-to)	571-578
Number of pages	8
Journal	Canadian Mathematical Bulletin
Volume	55
DOIs	https://doi.org/10.4153/CMB-2011-095-6
Publication status	Published - 2012

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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.",

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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.

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DO - 10.4153/CMB-2011-095-6

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JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

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