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Elliptic Functions and Elliptic Integrals [PDF]

, 1997
This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the ...
Viktor Prasolov, Yuri Solovyev
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Elliptic integrals, theta functions and elliptic functions

1966
General remarks. Any integral of the type ∫ R \(\left( {z,{Z^{\frac{1}{2}}}} \right)\) 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.
Wilhelm Magnus, Fritz Oberhettinger, Raj Pal Soni   +2 more
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On Computing Elliptic Integrals and Functions

Journal of Mathematics and Physics, 1965
Elliptic integral and function direct computation method using successive quadratic Landen and Gauss ...
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Equivariant functions and integrals of elliptic functions

Geometriae Dedicata, 2011
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Sebbar, Abdellah, Sebbar, Ahmed
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Numerical calculation of elliptic integrals and elliptic functions

Numerische Mathematik, 1965
Methoden (unter Benutzung der Landen- und Gauß-Transformation) und ALGOL 60-Programme zur Berechnung elliptischer Integrale 1., 2. und 3. Art für reelles Argument und 1. und 2. Art für komplexes Argument, wobei auf möglichst rasche Berechnung im Bereich \(0.001\leq k' \leq 1000\) Wert gelegt wird.
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Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals

SIAM Journal on Mathematical Analysis, 1992
The authors obtain a number of inequalities for the classical \(_ 2F_ 1\) hypergeometric functions and for two of its special cases, the complete elliptic integrals of the first and second kind.
Anderson, G. D., Vamanamurthy, M. K., Vuorinen, M.   +2 more
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Elliptic integral functions

2017
The functions named in the title of this chapter have attracted the interest of several famous mathematicians, among them Abel, Euler, Gauss, Hermite, Jacobi, Kronecker, Lagrange, Legendre, Ramanujan, Riemann, and Weierstrass. Their properties are well-chronicled in several books, including [AS64, Chapter 17], [Law89], [OLBC10, Chapter 19], [Wal96 ...
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Elliptic functions and integrals

2011
Abstract This chapter examines Riemann surfaces of genus 1. The constructions give an important model for the more general theory to be developed in Part III. The constructions also involve classical topics in mathematics, which relate the abstractions of Riemann surface theory to their origin in concrete calculus problems.
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Recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals

Applied Mathematics and Computation, 2013
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