On a new class of summation formulae involving the Laguerre polynomial

Yong S. Kim, Arjun K. Rathie, Richard B. Paris

Research output: Contribution to journal › Article

4 Citations (Scopus)
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Abstract

By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whipple’s theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293–300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appeared in the literature. Several related results due to Exton have also been given in a corrected form.
Original languageEnglish
Pages (from-to) 435-444
Number of pages10
JournalIntegral Transforms and Special Functions
Volume23
Issue number6
DOIs
Publication statusPublished - 2012

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Summation Formula
Laguerre Polynomials
Polynomials
Theorem
Summation
Generalized Hypergeometric Function
Gauss
Manipulation
Series
Class

Cite this

Kim, Yong S. ; Rathie, Arjun K. ; Paris, Richard B. / On a new class of summation formulae involving the Laguerre polynomial. In: Integral Transforms and Special Functions. 2012 ; Vol. 23, No. 6. pp. 435-444 .
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Kim, YS, Rathie, AK & Paris, RB 2012, 'On a new class of summation formulae involving the Laguerre polynomial', Integral Transforms and Special Functions, vol. 23, no. 6, pp. 435-444 . https://doi.org/10.1080/10652469.2011.597390

On a new class of summation formulae involving the Laguerre polynomial. / Kim, Yong S.; Rathie, Arjun K.; Paris, Richard B.

In: Integral Transforms and Special Functions, Vol. 23, No. 6, 2012, p. 435-444 .

Research output: Contribution to journal › Article

TY - JOUR

T1 - On a new class of summation formulae involving the Laguerre polynomial

AU - Kim, Yong S.

AU - Rathie, Arjun K.

AU - Paris, Richard B.

PY - 2012

Y1 - 2012

N2 - By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whipple’s theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293–300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appeared in the literature. Several related results due to Exton have also been given in a corrected form.

AB - By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whipple’s theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293–300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appeared in the literature. Several related results due to Exton have also been given in a corrected form.

U2 - 10.1080/10652469.2011.597390

DO - 10.1080/10652469.2011.597390

M3 - Article

VL - 23

SP - 435

EP - 444

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

SN - 1065-2469

IS - 6

ER -

Kim YS, Rathie AK, Paris RB. On a new class of summation formulae involving the Laguerre polynomial. Integral Transforms and Special Functions. 2012;23(6): 435-444 . https://doi.org/10.1080/10652469.2011.597390

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