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

单词

Weierstraß Zeta Function

释义

Weierstraß Zeta Function

The Quasiperiodic Function defined by

(1)

with

(2)

Then


			(3)

(4)

is an Odd Function. Integrating

gives

(5)

Letting

gives

, so

. Similarly,

. From Whittaker and Watson (1990),

(6)

If , then

(7)

Also,

(8)

(Whittaker and Watson 1990, p. 446).

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Weierstrass Elliptic and Related Functions.'' Ch. 18 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 627-671, 1972.

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.

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