Topic
Elliptic integral
About: Elliptic integral is a research topic. Over the lifetime, 1833 publications have been published within this topic receiving 38577 citations.
Papers published on a yearly basis
1 / 3
Papers
1,135 citations
Book•
1 Jan 1989
TL;DR: In this paper, Jacobi's Zeta and Epsilon functions are presented as functions of the squared modulus of the Equation (1) of the Squared Modulus.
Abstract: 1 Theta Functions.- 2 Jacobi's Elliptic Functions.- 3 Elliptic Integrals.- 4 Geometrical Applications.- 5 Physical Applications.- 6 Weierstrass's Elliptic Function.- 7 Applications of the Weierstrass Functions.- 8 Complex Variable Analysis.- 9 Modular Transformations..- Appendix A Fourier Series for a Periodic Analytic Function.- Appendix B Calculation of a Definite Integral.- Appendix C BASIC Program for Reduction of Elliptic Integral to Standard Form.- Appendix D Computation of Tables.- Table A. Theta Functions.- Table B. Nome and Complete Integrals of the First and Second Kinds as Functions of the Squared Modulus.- Table D. Legendre's Incomplete Integrals of First and Second Kinds.- Table E. Jacobi's Zeta and Epsilon Functions.- Table F. Sigma Functions.
923 citations
Book•
1 May 1990
TL;DR: In this paper, the authors present general theorems about elliptic functions Modular functions The Weierstrass functions Theta functions The Jacobi functions Transformation of Elliptic functions Additional facts about Elliptical integrals Some conformal mappings Extremal properties of fractions to which a transformation of elliptic function reduces Generalization of Tchebycheff polynomials Various supplements and applications.
Abstract: General theorems about elliptic functions Modular functions The Weierstrass functions Theta functions The Jacobi functions Transformation of elliptic functions Additional facts about elliptic integrals Some conformal mappings Extremal properties of fractions to which a transformation of elliptic functions reduces Generalization of Tchebycheff polynomials Various supplements and applications.
888 citations
Book•
1 Jul 1997
TL;DR: In this paper, the Gr/tzsch ring capacity estimates for the Gr /tzsch Ring Constant Bounds for Distortion Functions in the Plane are derived for quadruples and quasiconformal mappings.
Abstract: Basic functions: Hypergeometric Functions Gamma and Beta Functions Complete Elliptic Integrals The Arithmetic-Geometric Mean Quotients of Elliptic Integrals Jacobian Elliptic Functions and Conformal Maps. Conformal and quasiconformal mappings: Geometry of M/bius Transformations Conformal Invariants Quasiconformal Mappings Distortion Functions in the Plane. N-dimensional functions: The Gr/tzsch Ring Capacity Estimates for the Gr/tzsch Ring Constant Bounds for Distortion Functions. Applications: Quadruples and Quasiconformal Maps Distances and Quasiconformal Maps Inequalities for Conformal Invariants.
635 citations
Book•
14 Mar 2011TL;DR: In this paper, Jacobi's Triple-Product and some number theoretic applications are discussed, as well as algebraic approximations of the elementary functions of pi and arithmetic-geometric mean iterators.
Abstract: Complete Elliptic Integrals and the Arithmetic-Geometric Mean Iteration. Theta Functions and the Arithmetic-Geometric Mean Iteration. Jacobi's Triple-Product and Some Number Theoretic Applications. Higher Order Transformations. Modular Equations and Algebraic Approximations to pi. The Complexity of Algebraic Functions. Algorithms for the Elementary Functions. General Means and Iterations. Some Additional Applications. Other Approaches to the Elementary Functions. Pi. Bibliography. Symbol List. Index.
595 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 13 |
| 2024 | 16 |
| 2023 | 38 |
| 2022 | 85 |
| 2021 | 59 |
| 2020 | 61 |