Some summation formulas for the series

Author:
J.-L. Lavoie

Journal:
Math. Comp. **49** (1987), 269-274

MSC:
Primary 33A30; Secondary 33A15

DOI:
https://doi.org/10.1090/S0025-5718-1987-0890268-1

MathSciNet review:
890268

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Abstract | References | Similar Articles | Additional Information

Abstract: Summation formulas, contiguous to Watson's and Whipple's theorems in the theory of the generalized hypergeometric series, are obtained. Certain limiting cases of these results are given.

**[1]**W. N. Bailey,*Generalized Hypergeometric Series*, Cambridge Univ. Press, Cambridge, 1935.**[2]**G. H. Hardy, "A chapter from Ramanujan's note-book,"*Proc. Cambridge Philos. Soc.*, v. 21, 1923, pp. 492-503.**[3]**E. E. Kummer, "Über die hypergeometrische Reihe ,"*J. Reine Angew. Math.*, v. 15, 1836, pp. 127-172.**[4]**J. L. Lavoie, "Some evaluations for the generalized hypergeometric series,"*Math. Comp.*, v. 46, 1986, pp. 215-218. MR**815842 (87c:33007)****[5]**E. D. Rainville,*Special Functions*, Macmillan, New York, 1960. MR**0107725 (21:6447)****[6]**G. N. Watson, "The integral formula for generalized Legendre functions,"*Proc. London Math. Soc.*(2), v. 17, 1917, pp. 241-246.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1987-0890268-1

Keywords:
Generalized hypergeometric functions of one variable,
gamma function,
psi function

Article copyright:
© Copyright 1987
American Mathematical Society