A NEW PROOF OF SAALSCHÜTZ'S THEOREM FOR THE SERIES 3F2(1) AND ITS CONTIGUOUS RESULTS WITH APPLICATIONS
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The aim of this paper is to establish the well-known and very useful classical Saalsch$\ddot{u}$tz's theorem for the series $_3F_2$(1) by following a different method. In addition to this, two summation formulas closely related to the Saalsch$\ddot{u}$tz's theorem have also been obtained. The results established in this paper are further utilized to show how one can obtain certain known and useful hypergeometric identities for the series $_3F_2$(1) and $_4F_3(1)$ already available in the literature.
Abstract
The aim of this paper is to establish the well-known and very useful classical Saalsch$\ddot{u}$tz's theorem for the series $_3F_2$(1) by following a different method. In addition to this, two summation formulas closely related to the Saalsch$\ddot{u}$tz's theorem have also been obtained. The results established in this paper are further utilized to show how one can obtain certain known and useful hypergeometric identities for the series $_3F_2$(1) and $_4F_3(1)$ already available in the literature.
참고문헌 (6)
- K. Arora, "Some summation formulas for the series 3F2", Math. Ed, 28(2), pp.111~112 (1994)
- A. Erdelyi, "Tables of Integral Transforms. Vol. 2" (1954), McGraw Hill
- Y. S. Kim, "On a summation formula for the Clausen's series 3F2 with applications", Miskolc Math. Notes, 10(2), pp.145~153 (2009)
- E. D. Rainville, "Special Functions" (1960), The Macmillan Company
- L. J. Slater, "Generalized Hypergeometric Functions" (1966), Cambridge University Press
- F. J. W. Whipple, "Well-poised series and other generalized hypergeometric series", Proc. London Math. Soc, 25(2), pp.525~544 (1926)