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Chu, Wenchang

Terminating \(_2F_1(4)\)-series perturbed by two integer parameters. (English) Zbl 1352.33001

Proc. Am. Math. Soc. 145, No. 3, 1031-1040 (2017).
Summary: By means of generating functions and the linearization method, we establish analytical formulae for a class of terminating \( _2F_1(4)\)-series perturbed by two integer parameters. Under the Pfaff transformation, these formulae confirm, unexpectedly, a conjecture about evaluation of the \( _2F_1(-3)\)-series made by M. Apagodu and D. Zeilberger [Integers 8, No. 1, Article A36, 6 p. (2008; Zbl 1210.33024)].

Cited in 12 Documents

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
05A19 Combinatorial identities, bijective combinatorics

Keywords:

terminating hypergeometric series; generating function; linearization method; Chu-Vandermonde formula; Kummer’s summation theorem; Pfaff transformation

Citations:

Zbl 1210.33024

Software:

BruteTwoFone
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Full Text: DOI

References:

[1] Apagodu, Moa; Zeilberger, Doron, Searching for strange hypergeometric identities by sheer brute force, Integers, 8, A36, 6 pp. (2008) · Zbl 1210.33024
[2] kn:baileyW. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935. · Zbl 0011.02303
[3] Chu, Wenchang, Terminating hypergeometric \(_2F_1(2)\)-series, Integral Transforms Spec. Funct., 22, 2, 91-96 (2011) · Zbl 1215.33001 · doi:10.1080/10652469.2010.498112
[4] Chu, Wenchang, Analytical formulae for extended \(_3F_2\)-series of Watson-Whipple-Dixon with two extra integer parameters, Math. Comp., 81, 277, 467-479 (2012) · Zbl 1236.33013 · doi:10.1090/S0025-5718-2011-02512-3
[5] kn:doronS. B. Ekhad, Forty strange computer-discovered and computer-proved (of course) hypergeometric series evaluations, url: http://www.math.rutgers.edu/ zeilberg/ekhad/ekhad.html
[6] Gessel, Ira M., Finding identities with the WZ method, J. Symbolic Comput., 20, 5-6, 537-566 (1995) · Zbl 0908.33004 · doi:10.1006/jsco.1995.1064
[7] Slater, Lucy Joan, Generalized hypergeometric functions, xiii+273 pp. (1966), Cambridge University Press, Cambridge · Zbl 0135.28101
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