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

单词

Clausen Function

释义

Clausen Function

Define

			(1)
			(2)

and write

(3)

Then the Clausen function

can be given symbolically in terms of the Polylogarithm as

For

, the function takes on the special form

(4)

and for

, it becomes Clausen's Integral

(5)

The symbolic sums of opposite parity are summable symbolically, and the first few are given by

			(6)
			(7)
			(8)
			(9)
			(10)

for

(Abramowitz and Stegun 1972).

See also Clausen's Integral, Polygamma Function, Polylogarithm

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Clausen's Integral and Related Summations'' §27.8 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 1005-1006, 1972.

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 783, 1985.

Clausen, R. ``Über die Zerlegung reeller gebrochener Funktionen.'' J. reine angew. Math. 8, 298-300, 1832.

Grosjean, C. C. ``Formulae Concerning the Computation of the Clausen Integral .'' J. Comput. Appl. Math. 11, 331-342, 1984.

Jolley, L. B. W. Summation of Series. London: Chapman, 1925.

Wheelon, A. D. A Short Table of Summable Series. Report No. SM-14642. Santa Monica, CA: Douglas Aircraft Co., 1953.

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