Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind

DOI10.1016/S0001-8708(02)00054-3zbMath1018.33015MaRDI QIDQ1869022

Heng Huat Chan, Zhi-Guo Liu

Publication date: 9 April 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

incomplete elliptic integrals

Mathematics Subject Classification ID

Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items (7)

Inequalities and infinite product formula for Ramanujan generalized modular equation function ⋮ Cubic elliptic functions ⋮ An addition formula for the Jacobian theta function and its applications ⋮ Eisenstein series and theta functions to the septic base ⋮ EISENSTEIN SERIES TO THE TREDECIC BASE ⋮ Precise estimates for the solution of Ramanujan's generalized modular equation ⋮ On the points of order 3 of the period parallelogram of the Weierstrass elliptic function

Cites Work

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• Representations of integers as sums of squares
• On an identity of Ramanujan based on the hypergeometric series \(_2F_1(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)\)
• Representations of integers as sums of 32 squares
• Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions
• On a Definite Integral of a Hypergeometric Function
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• On Ramanujan's quartic theory of elliptic functions

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