Bailey,s Theorem
المؤلف:
Bailey, W. N.
المصدر:
"The Partial Sum of the Coefficients of the Hypergeometric Series." J. London Math. Soc. 6,
الجزء والصفحة:
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21-5-2019
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Bailey's Theorem
Let 
be the gamma function and 
denote a double factorial, then
Writing the sums explicitly, Bailey's theorem states
REFERENCES:
Bailey, W. N. "The Partial Sum of the Coefficients of the Hypergeometric Series." J. London Math. Soc. 6, 40-41, 1931.
Bailey, W. N. "On One of Ramanujan's Theorems." J. London Math. Soc. 7, 34-36, 1932.
Darling, H. B. C. "On a Proof of One of Ramanujan's Theorems." J. London Math. Soc. 5, 8-9, 1930.
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 106-107 and 112, 1999.
Hodgkinson, J. "Note on One of Ramanujan's Theorems." J. London Math. Soc. 6, 42-43, 1931.
Watson, G. N. "Theorems Stated by Ramanujan (VIII): Theorems on Divergent Series." J. London Math. Soc. 4, 82-86, 1929.
Watson, G. N. "The Constants of Landau and Lebesgue." Quart. J. Math. (Oxford) 1, 310-318, 1930.
Whipple, F. J. W. "The Sum of the Coefficients of a Hypergeometric Series." J. London Math. Soc. 5, 192, 1930.
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