Efficient evaluation of incomplete elliptic integrals and functions
نویسندگان
چکیده
منابع مشابه
Recursive 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 کاملFast 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 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.
متن کاملClosed-Form Bounds to the Rice and Incomplete Toronto Functions and Incomplete Lipschitz-Hankel Integrals
This article provides novel analytical results for the Rice function, the incomplete Toronto function and the incomplete Lipschitz-Hankel Integrals. Firstly, upper and lower bounds are derived for the Rice function, Ie(k, x). Secondly, explicit expressions are derived for the incomplete Toronto function, TB(m,n, r), and the incomplete Lipschitz-Hankel Integrals of the modified Bessel function o...
متن کاملTable of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric R-functions
Any product of real powers of Jacobian elliptic functions can be written in the form csm1 (u, k) ds2 (u, k) nsm3 (u, k). If all three m’s are even integers, the indefinite integral of this product with respect to u is a constant times a multivariate hypergeometric function R−a(b1, b2, b3; x, y, z) with halfodd-integral b’s and −a + b1 + b2 + b3 = 1, showing it to be an incomplete elliptic integ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1988
ISSN: 0898-1221
DOI: 10.1016/0898-1221(88)90010-7