This chapter focuses on the elliptic integrals and functions. An elliptic integral is an integral of the form ∫ R ( x, √ P ( x )) dx , in which R is a rational function of its arguments and P(x) is a third- or
Elliptic Integrals and Elliptic Functions 作者:Takashi Takebe 出版社:Springer 副标题:Moscow Lectures (ML, volume 9) 出版年:2023-5 丛书:Moscow Lectures ISBN:9783031302640 豆瓣评分 目前无人评价 内容简介· ··· This book gives a comprehensive introduction to those parts of the theory of elliptic...
elliptic functions and elliptic integrals 美国数学会翻译出版 椭圆函数，与那么多数学大师的名字联系在一...
elliptic functionsarithmetic geometric meanincomplete elliptic integralstheta functionsComplete Integrals of the First and Second KindIncomplete Elliptic IntegralsElliptic Functions and Theta FunctionsNumerical AspectsRemarks and Comments for Further ReadingExercises and Further Examples...
1960, Page 161 References to Chapter 8-ELLIPTIC INTEGRALS AND ELLIPTIC FUNCTIONS Author links open overlay panel, Show more Add to Mendeley Share Cite https://doi.org/10.1016/B978-0-08-009244-7.50030-3Get rights and content Access through your organization ...
Functions Related Guides Tech Notes Elliptic IntegralsWith careful standardization of argument conventions, the Wolfram Language provides full coverage of elliptic integrals, with arbitrary-precision numerical evaluation for complex values of all parameters, as well as extensive symbolic transformations and si...
General remarks . Any integral of the type ∫ R \\(\\left( {z,{Z^{\\frac{1}{2}}} ight)\\) is a rational function of x and y and Z is a polynomial of the third or fourth degree in z with real coefficients and no repeated factors is called an elliptic integral.doi...
The meaning of ELLIPTIC INTEGRAL is the integral as to x of a function rational in x and the square root of a polynomial of third or fourth degree in x.
V. The Direct Numerical Calculation of Elliptic Functions and Integrals. London: Cambridge University Press, 1924.Prasolov, V. and Solovyev, Y. Elliptic Functions and Elliptic Integrals. Providence, RI: Amer. Math. Soc., 1997.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and ...
For simplicity, all indefinite integrals in this article omit the integral constant +C . Several different notations are used for these special functions; in this article, these notations and definitions are adopted. k′=1−k2 where k2<1 Complete elliptic integrals of the first kindK(k)≡π...