Numerical computation of real or complex elliptic integrals
نویسندگان
چکیده
منابع مشابه
Fast Computation of Complete Elliptic Integrals and Jacobian Elliptic Functions
As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9 to 19 obtained by truncating Taylor series exp...
متن کاملNumerical computation of inverse complete elliptic integrals of first and second kinds
We developed the numerical procedures to evaluate the inverse functions of the complete elliptic integrals of the first and second kind, K(m) and E(m), with respect to the parameter m. The evaluation is executed by inverting eight sets of the truncated Taylor series expansions of the integrals in terms of m or of − log(1 −m). The developed procedures are (1) so precise that the maximum absolute...
متن کاملThree Improvements in Reduction and Computation of Elliptic Integrals
Three improvements in reduction and computation of elliptic integrals are made. 1. Reduction formulas, used to express many elliptic integrals in terms of a few standard integrals, are simplified by modifying the definition of intermediate "basic integrals." 2. A faster than quadratically convergent series is given for numerical computation of the complete symmetric elliptic integral of the thi...
متن کاملRecursive computation of derivatives of elliptic functions and of incomplete elliptic integrals
Presented are the recurrence formulas to compute the derivatives of a general elliptic function, Weierstrass’s ℘ function, the Jacobian elliptic functions, and the incomplete elliptic integrals in the forms of Jacobi and Legendre with respect to the argument or the amplitude. The double precision computation by the formulas is correct with 15 digits or so for the first 10 orders of differentiat...
متن کاملIntegrals involving complete elliptic integrals
We give a closed-form evaluation of a number of Erd elyi-Kober fractional integrals involving elliptic integrals of the rst and second kind, in terms of the 3F2 generalized hypergeometric function. Reduction formulae for 3F2 enable us to simplify the solutions for a number of particular cases. c © 1999 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Numerical Algorithms
سال: 1995
ISSN: 1017-1398,1572-9265
DOI: 10.1007/bf02198293