“Glaisher-Kinkelin Constant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Glaisher-Kinkelin Constant

释义

Glaisher-Kinkelin Constant

N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.

Define

			(1)

			(2)

where

is the G-Function and

is the K-Function. Then

(3)

(4)

where

(5)

where

is the Riemann Zeta Function,

is Pi, and

is the Euler-Mascheroni Constant (Kinkelin 1860, Glaisher 1877, 1878, 1893, 1894). Glaisher (1877) also obtained

(6)

Glaisher (1894) showed that

(7)

(8)

(9)

where

(10)

See also G-Function, Hyperfactorial, K-Function

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/glshkn/glshkn.html

Glaisher, J. W. L. ``On a Numerical Continued Product.'' Messenger Math. 6, 71-76, 1877.

Glaisher, J. W. L. ``On the Product .'' Messenger Math. 7, 43-47, 1878.

Glaisher, J. W. L. ``On Certain Numerical Products.'' Messenger Math. 23, 145-175, 1893.

Glaisher, J. W. L. ``On the Constant which Occurs in the Formula for .'' Messenger Math. 24, 1-16, 1894.

Kinkelin. ``Über eine mit der Gammafunktion verwandte Transcendente und deren Anwendung auf die Integralrechnung.'' J. Reine Angew. Math. 57, 122-158, 1860.

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