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

单词

Elliptic Alpha Function

释义

Elliptic Alpha Function

Elliptic alpha functions relate the complete Elliptic Integrals of the First andSecond Kinds at Elliptic Integral Singular Values according to

			(1)
			(2)
			(3)

where

is a Theta Function and

			(4)
			(5)

and

is the Elliptic Lambda Function. The elliptic alpha function is related to the Elliptic DeltaFunction by

(6)

It satisfies

(7)

and has the limit

(8)

(Borwein et al. 1989). A few specific values (Borwein and Borwein 1987, p. 172) are

J. Borwein has written an Algorithm which uses lattice basis reduction to provide algebraic values for .

See also Elliptic Integral of the First Kind, Elliptic Integral of the Second Kind,Elliptic Integral Singular Value, Elliptic Lambda Function

References

Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, 1987.

Borwein, J. M.; Borwein, P. B.; and Bailey, D. H. ``Ramanujan, Modular Equations, and Approximations to Pi, or How to Compute One Billion Digits of Pi.'' Amer. Math. Monthly 96, 201-219, 1989.

Weisstein, E. W. ``Elliptic Singular Values.'' Mathematica notebook EllipticSingular.m.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。