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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.
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.
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.
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 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 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 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.
CERTAIN SUMMATION FORMULAS DUE TO RAMANUJAN AND THEIR GENERALIZATIONS
RATHIE ARJUN K.,MALANI SHALOO,MATHUR RACHANA,CHOI JUNESANG Korean Mathematical Society 2005 대한수학회보 Vol.42 No.3
The authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan. The results are derived with the help of generalized Dixon's theorem obtained earlier by Lavoie, Grondin, Rathie, and Arora.
Certain summation formulas due to Ramanujan and their generalizations
Arjun K. Rathie,Shaloo Malani,Rachana Mathur,최준상 대한수학회 2005 대한수학회보 Vol.42 No.3
The authors aim at deriving four generalized summationformulas, which, upon specializing their parameters, give manysummation identities including, especially, the four veryinteresting summation formulas due to Ramanujan. The results arederived with the help of generalized Dixon's theorem obtained earlier by Lavoie, Grondin, Rathie, and Arora.
On a New Class of Double Integrals Involving Hypergeometric Function
A.K. Rathie ...et al KYUNGPOOK UNIVERSITY 1999 Kyungpook mathematical journal Vol.39 No.2
The aim of this research is to provide twenty five double integrals involving hypergeometric function in the form of a single integral. Fifty two integrals follow as special cases of our main findings. These results are obtained with the help of a contiguous extension of Watson's theorem on the sum of a ₃F₂recently obtained by Lavoie, Grondin and Rathie, and an interesting integral given in Edwards. The double integrals derived in this paper are simple, interesting, easily established and may be useful.