Certain hypergeometric identities deducible by using the beta integral method
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The main objective of this paper is to show how one can obtain eleven new and interesting hypergeometric identities in the form of a single result from the old ones by mainly employing the known beta integral method which was recently introduced and used in a systematic manner by Krattenthaler and Rao [6]. The results are derived with the help of a generalization of a well-known hypergeometric transformation formula due to Kummer. Several identities including one obtained earlier by Krattenthaler and Rao [6] follow as special cases of our main results.
Abstract
The main objective of this paper is to show how one can obtain eleven new and interesting hypergeometric identities in the form of a single result from the old ones by mainly employing the known beta integral method which was recently introduced and used in a systematic manner by Krattenthaler and Rao [6]. The results are derived with the help of a generalization of a well-known hypergeometric transformation formula due to Kummer. Several identities including one obtained earlier by Krattenthaler and Rao [6] follow as special cases of our main results.
참고문헌 (10)
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- A. Erdelyi, "Higher Transcendental Functions. Vols. I, II" (1953), McGraw-Hill Book Company
- C. Krattenthaler, "Automatic generation of hypergeometric identities by the beta integral method", J. Comput. Appl. Math, 160(1), pp.159~173 (2003)
- E. E. Kummer, "Uber die hypergeometrische Reihe", J. Reine Angew. Math, 15, pp.39~83 (1836)
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- E. D. Rainville, "Special Functions, Macmillan Company" (1971), Reprinted by Chelsea Publishing Company
- H. M. Srivastava, "ZETA AND q-ZETA FUNCTIONS AND ASSOCIATED SERIES AND INTEGRALS" (2012), Elsevier