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

单词

Central Beta Function

释义

Central Beta Function

The central beta function is defined by

(1)

where

is the Beta Function. It satisfies the identities

			(2)
			(3)
			(4)
			(5)

With

, the latter gives the Wallis Formula. When

(6)

where

(7)

The central beta function satisfies

(8)

(9)

(10)

(11)

For

an Odd Positive Integer, the central beta function satisfies theidentity

(12)

See also Beta Function, Regularized Beta Function

References

Borwein, J. M. and Zucker, I. J. ``Elliptic Integral Evaluation of the Gamma Function at Rational Values of Small Denominators.'' IMA J. Numerical Analysis 12, 519-526, 1992.

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