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

6 Citations (Scopus)
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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
Publication statusPublished - 2012

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Hypergeometric Series
Hypergeometric Functions
Reduction formula
Generalized Hypergeometric Function
Summation Formula
Series
Partial Sums
Summation
Gauss
Integer

Cite this

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. 2012 ; Vol. 23, No. 1. pp. 21-33.
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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. https://doi.org/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

TY - JOUR

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

Y1 - 2012

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.

U2 - 10.1080/10652469.2011.552263

DO - 10.1080/10652469.2011.552263

M3 - Article

VL - 23

SP - 21

EP - 33

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

SN - 1065-2469

IS - 1

ER -

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. https://doi.org/10.1080/10652469.2011.552263

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