“K-Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

K-Function

释义

K-Function

An extension of the -function

(1)

defined by

(2)

Here,

is the G-Function defined by

(3)

The -function is given by the integral

(4)

and the closed-form expression

(5)

where

is the Riemann Zeta Function,

its Derivative,

is theHurwitz Zeta Function, and

(6)

also has a Stirling-like series

(7)

where

			(8)
			(9)
			(10)

and

is the Euler-Mascheroni Constant (Gosper).

The first few values of for , 3, ... are 1, 4, 108, 27648, 86400000, 4031078400000, ... (Sloane's A002109). These numbers are called Hyperfactorials by Sloane and Plouffe (1995).

See also G-Function, Glaisher-Kinkelin Constant, Hyperfactorial, Stirling's Series

References

Sloane, N. J. A. SequenceA002109/M3706in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

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