Abstract
By combining a telescopic summation formula with Kummer-Thomae-Whipple transformation, we prove two nonterminating 3 F 2(1)-series identities with one of them confirming a conjecture by Milgram (2009) and another one extending a couple of terminating series identities due to Gessel and Stanton (1982).
[1] BAILEY, W. N.: Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935. Search in Google Scholar
[2] CHU, W.: Inversion techniques and combinatorial identities: strange evaluations of hypergeometric series, Pure Appl. Math. (Xian) 4 (1993), 409–428. Search in Google Scholar
[3] GESSEL, I.— STANTON, D.: Strange evaluations of hypergeometric series, SIAM J. Math. Anal. 13 (1982), 295–308. http://dx.doi.org/10.1137/051302110.1137/0513021Search in Google Scholar
[4] MILGRAM, M.: On hypergeometric 3F 2(1) — A review, ArXiv:math.CA/0603096; Updated version, 2009. Search in Google Scholar
[5] RAINVILLE, E. D.: Special Functions, Chelsea Publishing Co., Bronx, N.Y., 1971. Search in Google Scholar
© 2012 Mathematical Institute, Slovak Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
