“Modulus (Elliptic Integral)”的概念、定义、习题解题方法及翻译-数学辞典

单词

Modulus (Elliptic Integral)

释义

Modulus (Elliptic Integral)

A parameter used in Elliptic Integrals and Elliptic Functionsdefined to be , where is the Parameter. An Elliptic Integral is written whenthe modulus is used. It can be computed explicitly in terms of Theta Functions of zero argument:

(1)

The Real period

and Imaginary period

are given by

(2)

(3)

where

is a complete Elliptic Integral of the First Kind and the complementary modulus is defined by

(4)

with

the modulus.

See also Amplitude, Characteristic (Elliptic Integral), Elliptic Function, Elliptic Integral, Elliptic Integral Singular Value, Modular Angle, Nome,Parameter, Theta Function

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 590, 1972.

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