AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON

• Journal title : Honam Mathematical Journal
• Volume 32, Issue 1,  2010, pp.61-71
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2010.32.1.061
Title & Authors
AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON
Lee, Seung-Woo; Kim, Yong-Sup;

Abstract
The aim of this paper is to extend a number of transformation formulas for the four $\small{X_4}$, $\small{X_5}$, $\small{X_7}$, and $\small{X_8}$ among twenty triple hypergeometric series $\small{X_1}$ to $\small{X_{20}}$ introduced earlier by Exton. The results are derived from the generalized Kummer`s theorem and Dixon`s theorem obtained earlier by Lavoie et al..
Keywords
Triple hypergeometric series;Generalized Kummer`s theorem for $\small{_2F_1(-1)}$;Generalized Dixon`s summation theorem for $\small{_3F_2(1)}$;
Language
English
Cited by
1.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION \$X_2\$,;;;

한국수학교육학회지시리즈B:순수및응용수학, 2010. vol.17. 4, pp.347-354
2.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5,;;;

호남수학학술지, 2010. vol.32. 3, pp.389-397
3.
GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION,;;;

호남수학학술지, 2011. vol.33. 1, pp.43-50
4.
DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS,;;;

충청수학회지, 2011. vol.24. 4, pp.745-758
5.
GENERALIZED SINGLE INTEGRAL INVOLVING KAMP\$\acute{E}\$ DE F\$\acute{E}\$RIET FUNCTION,;;;

충청수학회지, 2011. vol.24. 2, pp.205-212
6.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8,;;;

대한수학회논문집, 2012. vol.27. 2, pp.257-264
1.
GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION, Honam Mathematical Journal, 2011, 33, 1, 43
2.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8, Communications of the Korean Mathematical Society, 2012, 27, 2, 257
3.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5, Honam Mathematical Journal, 2010, 32, 3, 389
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