Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x)

A. R. Miller, Richard B. Paris

Research output: Contribution to journal › Article

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Abstract

We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer. The results derived for the latter are used to obtain Kummer-type transformations for the generalized hypergeometric function 2 F 2(x) and reduction formulas for certain Kampé de Fériet functions. Certain summations for the partial sums of the Gauss hypergeometric series 2 F 1(1) are also obtained.
Original languageEnglish
Pages (from-to)21-33
Number of pages13
JournalIntegral Transforms and Special Functions
Volume23
Issue number1
DOIs
StatePublished - 2012

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Hypergeometric series
Kampé de Fériet functions
Reduction formula
Generalized hypergeometric function
Summation formula
Hypergeometric functions
Partial sums
Summation
Gauss
Integer
Series

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Miller, A. R.; Paris, Richard B. / Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x).

In: Integral Transforms and Special Functions, Vol. 23, No. 1, 2012, p. 21-33.

Research output: Contribution to journal › Article

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title = "Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x)",
abstract = "We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer. The results derived for the latter are used to obtain Kummer-type transformations for the generalized hypergeometric function 2 F 2(x) and reduction formulas for certain Kampé de Fériet functions. Certain summations for the partial sums of the Gauss hypergeometric series 2 F 1(1) are also obtained.",
author = "Miller, {A. R.} and Paris, {Richard B.}",
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doi = "10.1080/10652469.2011.552263",
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journal = "Integral Transforms and Special Functions",
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Miller, AR & Paris, RB 2012, 'Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x)' Integral Transforms and Special Functions, vol 23, no. 1, pp. 21-33. DOI: 10.1080/10652469.2011.552263

Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x). / Miller, A. R.; Paris, Richard B.

In: Integral Transforms and Special Functions, Vol. 23, No. 1, 2012, p. 21-33.

Research output: Contribution to journal › Article

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T1 - Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x)

AU - Miller,A. R.

AU - Paris,Richard B.

PY - 2012

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N2 - We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer. The results derived for the latter are used to obtain Kummer-type transformations for the generalized hypergeometric function 2 F 2(x) and reduction formulas for certain Kampé de Fériet functions. Certain summations for the partial sums of the Gauss hypergeometric series 2 F 1(1) are also obtained.

AB - We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer. The results derived for the latter are used to obtain Kummer-type transformations for the generalized hypergeometric function 2 F 2(x) and reduction formulas for certain Kampé de Fériet functions. Certain summations for the partial sums of the Gauss hypergeometric series 2 F 1(1) are also obtained.

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DO - 10.1080/10652469.2011.552263

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JO - Integral Transforms and Special Functions

T2 - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

SN - 1065-2469

IS - 1

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Miller AR, Paris RB. Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x). Integral Transforms and Special Functions. 2012;23(1):21-33. Available from, DOI: 10.1080/10652469.2011.552263

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