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OTHER PROOFS OF KUMMER'S SECOND THEOREM
Malani, Shaloo,Choi, June-Sang The Youngnam Mathematical Society Korea 2001 East Asian mathematical journal Vol.17 No.1
The aim of this research note is to derive the well known Kummer's second theorem by transforming the integrals which represent some generalized hypergeometric functions. This theorem can also be shown by combining two known Bailey's and Preece's identities for the product of generalized hypergeometric series.
Generalizations of Dixon's and Whipple's Theorems on the Sum of a <sub>3</sub>F<sub>2</sub>
Choi, Junesang,Malani, Shaloo,Rathie, Arjun K. Department of Mathematics 2007 Kyungpook mathematical journal Vol.47 No.3
InIn this paper we consider generalizations of the classical Dixon's theorem and the classical Whipple's theorem on the sum of a $_3F_2$. The results are derived with the help of generalized Watson's theorem obtained earlier by Mitra. A large number of results contiguous to Dixon's and Whipple's theorems obtained earlier by Lavoie, Grondin and Rathie, and Lavoie, Grondin, Rathie and Arora follow special cases of our main findings.
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.
최준상,Arjun K. Rathie,Shaloo Malani,Rachana Mathur 한국수학교육학회 2006 純粹 및 應用數學 Vol.13 No.4
In 194, Lavoie et al. have obtained twenty tre interesting resultsclosely related to the clasical Dixon’s theorem on the sum of a 3F2 by making asystematic use of some known relations among contiguous functions. We aim atshowing that hese results can be derived by using the same te chnique developedby Bailey with the help of Gaus’s umation theorem and gene ralized Kumer’stheorem obtained by Lavoie et al..
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.
A SUMMATION FORMULA OF <sub>6</sub>F<sub>5</sub>(1)
Choi, June-Sang,Arjun K.,Shaloo Malani Korean Mathematical Society 2004 대한수학회논문집 Vol.19 No.4
The authors aim at obtaining an interesting result for a special summation formula for $_{6F_5}$(1), by comparing two generalized Watson's theorems on the sum of a $_{3F_2}$ obtained earlier by Mitra and Lavoie et. al.