Barnes,Lemma
المؤلف:
Barnes, E. W.
المصدر:
A New Development in the Theory of the Hypergeometric Functions." Proc. London Math. Soc. 6
الجزء والصفحة:
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21-5-2019
2285
Barnes' Lemma
If a contour in the complex plane is curved such that it separates the increasing and decreasing sequences of poles, then
where 
is the gamma function (Bailey 1935, p. 7).
Barnes' second lemma states that
provided that 
(Bailey 1935, pp. 42-43).
REFERENCES:
Bailey, W. N. "Barnes' Lemma" and "Barnes' Second Lemma." §1.7 and 6.2 in Generalised Hypergeometric Series. Cambridge, England: University Press, pp. 7 and 42-43, 1935.
Barnes, E. W. "A New Development in the Theory of the Hypergeometric Functions." Proc. London Math. Soc. 6, 141-177, 1908.
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