Series expansions of symmetric elliptic integrals

Related Items (5)

An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions ⋮ Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions ⋮ Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind ⋮ Fast computation of a general complete elliptic integral of third kind by half and double argument transformations ⋮ Uniform approximations of the first symmetric elliptic integral in terms of elementary functions

Uses Software

DLMF
NSWC
algorithm 577

Cites Work

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Fast computation of complete elliptic integrals and Jacobian elliptic functions
Precise computation of acceleration due to uniform ring or disk
Fast computation of incomplete elliptic integral of first kind by half argument transformation
Computing elliptic integrals by duplication
Numerical computation of incomplete elliptic integrals of a general form
Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity
Numerical calculation of elliptic integrals and elliptic functions.II
Numerical calculation of elliptic integrals and elliptic functions
Normal elliptic integrals of the first and second kinds
An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind
Numerical calculation of elliptic integrals and elliptic functions. III
On the numerical calculation of elliptic integrals of the first and second kind and the elliptic functions of Jacobi
Series expansions for the third incomplete elliptic integral via partial fraction decompositions
Asymptotic Expansion of the First Elliptic Integral
Elliptic Integrals of the First Kind
Short Proofs of Three Theorems on Elliptic Integrals
Asymptotic Approximations for Symmetric Elliptic Integrals
Asymptotic Expansions of Symmetric Standard Elliptic Integrals
Chebyshev Polynomial Expansions of Complete Elliptic Integrals
Symmetric standard elliptic integrals with two or three large parameters
Chebyshev Approximations for the Complete Elliptic Integrals K and E
On Computing Elliptic Integrals and Functions
Approximations for Elliptic Integrals
Rational Approximations to the Incomplete Elliptic Integrals of the First and Second Kinds
On the Series Expansion Method for Computing Incomplete Elliptic Integrals of the First and Second Kinds
Further Approximations for Elliptic Integrals
Symmetric Elliptic Integrals of the Third Kind
New Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind
Uniform asymptotic expansions of symmetric elliptic integrals

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