“q-Gamma Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

q-Gamma Function

释义

q-Gamma Function

A q-Analog of the Gamma Function defined by

(1)

where

is a q-Series. The

-gamma function satisfies

(2)

(Andrews 1986).

A curious identity for the functional equation


	(3)

where

(4)

is given by

(5)

for any

See also q-Beta Function, q-Factorial

References

Andrews, G. E. ``W. Gosper's Proof that .'' Appendix A in -Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. Providence, RI: Amer. Math. Soc., p. 11 and 109, 1986.

Wenchang, C. Problem 10226 and Solution. ``A -Trigonometric Identity.'' Amer. Math. Monthly 103, 175-177, 1996.

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