Some summation formulas for the series
Author:
J.L. Lavoie
Journal:
Math. Comp. 49 (1987), 269274
MSC:
Primary 33A30; Secondary 33A15
MathSciNet review:
890268
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Abstract 
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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.
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G. H. Hardy, "A chapter from Ramanujan's notebook," Proc. Cambridge Philos. Soc., v. 21, 1923, pp. 492503.
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E. E. Kummer, "Über die hypergeometrische Reihe ," J. Reine Angew. Math., v. 15, 1836, pp. 127172.
 [4]
J.L.
Lavoie, Some evaluations for the generalized
hypergeometric series, Math. Comp.
46 (1986), no. 173, 215–218. MR 815842
(87c:33007), http://dx.doi.org/10.1090/S00255718198608158429
 [5]
Earl
D. Rainville, Special functions, The Macmillan Co., 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. 241246.
 [1]
 W. N. Bailey, Generalized Hypergeometric Series, Cambridge Univ. Press, Cambridge, 1935.
 [2]
 G. H. Hardy, "A chapter from Ramanujan's notebook," Proc. Cambridge Philos. Soc., v. 21, 1923, pp. 492503.
 [3]
 E. E. Kummer, "Über die hypergeometrische Reihe ," J. Reine Angew. Math., v. 15, 1836, pp. 127172.
 [4]
 J. L. Lavoie, "Some evaluations for the generalized hypergeometric series," Math. Comp., v. 46, 1986, pp. 215218. 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. 241246.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708902681
PII:
S 00255718(1987)08902681
Keywords:
Generalized hypergeometric functions of one variable,
gamma function,
psi function
Article copyright:
© Copyright 1987
American Mathematical Society
