Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
New Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind
Journal of the ACM (JACM)
Algorithm 577: Algorithms for Incomplete Elliptic Integrals [S21]
ACM Transactions on Mathematical Software (TOMS)
The Mathematica Book
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
NIST Handbook of Mathematical Functions
NIST Handbook of Mathematical Functions
Journal of Computational and Applied Mathematics
Numerical inversion of a general incomplete elliptic integral
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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We developed a method to compute simultaneously two associate incomplete elliptic integrals of the second kind, B(@f|m) and D(@f|m), by the half argument formulas of Jacobian elliptic functions and the double argument transformations of the integrals. The relative errors of the new method are sufficiently small as 5-10 machine epsilons. Meanwhile, the new method runs 3-6 times faster than that using Carlson's R"D. As a result, it enables a precise and fast computation of arbitrary linear combination of the incomplete elliptic integrals of the first and the second kind, F(@f|m) and E(@f|m).