Abstract: Formulas involving the complete elliptic integrals K, E, and II occur in the calculation of standards of inductance and mutual inductance, in the calculation of the magnetic field components ...
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 ...
In this paper, we define four new examples of the non-elementary expo-elliptic functions. This is an exponential function whose exponent is the product of a real number and the upper limit of ...
In this paper, we show an elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind and generalize an interesting result of Alzer.
JacobiElliptic is an implementation of Toshio Fukushima's & Billie C. Carlson's for calculating Elliptic Integrals and Jacobi Elliptic Functions. The default algorithms are set to the Carlson ...
A collection of simple methods for computing some pseudo-elliptic and pseudo-hyperelliptic integrals
This is a Mathematica prototype for solving some pseudo-elliptic integrals in terms of elementary functions. Relative to the algebraic case of the Risch-Trager-Bronstein algorithm, its very simple, ...
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