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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.
ON SEVERAL NEW CONTIGUOUS FUNCTION RELATIONS FOR k-HYPERGEOMETRIC FUNCTION WITH TWO PARAMETERS
Chinra, Sivamani,Kamalappan, Vilfred,Rakha, Medhat A.,Rathie, Arjun K. Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.3
Very recently, Mubeen, et al. [6] have obtained fifteen contiguous function relations for k-hypergeometric functions with one parameter by the same technique developed by Gauss. The aim of this paper is to obtain seventy-two new and interesting contiguous function relations for k-hypergeometric functions with two parameters. Obviously, for $k{\rightarrow}1$ we recover the results obtained by Cho, et al. [2] and Rakha, et al. [8].
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.
( K. Shani ),( Junesang Choi ),( Arjun K. Rathie ) 호남수학회 2016 호남수학학술지 Vol.38 No.4
The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kum- mer using a differential equation approach.
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.
Rathie, Arjun K.,Kim, Yong-Sup,Choi, June-Sang Korean Mathematical Society 2006 대한수학회논문집 Vol.21 No.3
We aim mainly at presenting two generalizations of the well-known Gauss's second summation theorem and Bailey's formula for the series $_2F_1(1/2)$. An interesting transformation formula for $_pF_q$ is obtained by combining our two main results. Relevant connections of some special cases of our main results with those given here or elsewhere are also pointed out.
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.