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GENERALIZATION OF WHIPPLE'S THEOREM FOR DOUBLE SERIES
RATHIE, ARJUN K.,GAUR, VIMAL K.,KIM, YONG SUP,PARK, CHAN BONG The Honam Mathematical Society 2004 호남수학학술지 Vol.26 No.1
In 1965, Bhatt and Pandey have obtained an analogue of the Whipple's theorem for double series by using Watson's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty five results for double series closely related to the analogue of the Whipple's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty five summation formulas closely related to the Watson's theorem on the sum of a $_3F_2$ obtained recently by Lavoie, Grondin, and Rathie.
TWO GENERAL HYPERGEOMETRIC TRANSFORMATION FORMULAS
Choi, Junesang,Rathie, Arjun K. Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.4
A large number of summation and transformation formulas involving (generalized) hypergeometric functions have been developed by many authors. Here we aim at establishing two (presumably) new general hypergeometric transformations. The results are derived by manipulating the involved series in an elementary way with the aid of certain hypergeometric summation theorems obtained earlier by Rakha and Rathie. Relevant connections of certain special cases of our main results with several known identities are also pointed out.
Generalization of Whipple's theorem for double series
Arjun K. Rathie,Vimal K. Gaur,Yong Sup Kim,Chan Bong Park 호남수학회 2004 호남수학학술지 Vol.26 No.1
In 1965, Bhatt and Pandey have obtained an analogue of the Whipple's theorem for double series by using Watson's theo- rem on the sum of a 3F2. The aim of this paper is to derive twenty 칥e results for double series closely related to the analogue of the Whipple's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty 칥e summation for- mulas closely related to the Watson's theorem on the sum of a 3F2 obtained recently by Lavoie, Grondin, and Rathie.
APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES <sub>2</sub>F<sub>1</sub>
Kim, Yong-Sup,Rathie, Arjun K. Korean Mathematical Society 2009 대한수학회보 Vol.46 No.6
The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series $_3F_2$, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Lavoie, Grondin, and Rathie.
GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION
Kim, Yong-Sup,Ali, Shoukat,Rathie, Navratna The Honam Mathematical Society 2011 호남수학학술지 Vol.33 No.1
The aim of this paper is to obtain twenty five Eulerian type double integrals in the form of a general double integral involving Kamp$\'{e}$ de F$\'{e}$riet function. The results are derived with the help of the generalized classical Watson's theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.
Generalized double integral involving kampe de feriet function
( Yong Sup Kim ),( Shoukat Ali ),( Navratna Rathie ) 호남수학회 2011 호남수학학술지 Vol.33 No.1
The aim of this paper is to obtain twenty five Eulerian type double integrals in the form of a general double integral involving Kampe de Feriet function. The results are derived with the help of the generalized classical Watson`s theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.
GENERALIZED SINGLE INTEGRAL INVOLVING KAMP¶E DE F¶ERIET FUNCTION
Yong Sup Kim,Shoukat Ali,Navratna Rathie 충청수학회 2011 충청수학회지 Vol.24 No.2
The aim of this paper is to obtain twenty ¯ve Euleriantype single integrals in the form of a general single integral involving Kamp¶e de F¶eriet function. The results are derived with the help of the generalized classical Watson s theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.
RATHIE, ARJUN K.,KIM, YONG SUP 호남수학회 2006 호남수학학술지 Vol.28 No.2
A Kummer-type transformation formula for the generalized hypergeometric function $_2F_2$ deduced by Exton, rederived in two simple and transparent ways by Miller and generalized by Paris, is again derived by another method.
GENERALIZATION OF A TRANSFORMATION FORMULA FOUND BY BAILLON AND BRUCK
Rathie, Arjun K.,Kim, Yong-Sup Korean Mathematical Society 2008 대한수학회논문집 Vol.23 No.4
We aim mainly at presenting a generalization of a transformation formula found by Baillon and Bruck. The result is derived with the help of the well-known quadratic transformation formula due to Gauss.
A NOTE ON GENERALIZATIONS OF PREECE'S IDENTITY AND OTHER CONTIGUOUS RESULTS
Rathie, Arjun K.,Choi, June-Sang Korean Mathematical Society 1998 대한수학회보 Vol.35 No.2
The aim of this paper is to establish generalizations of the well known Preece's identity and other identities involving product of generalized hypergeometric series by using new and very short method.