Automatic reduction of elliptic integrals using Carlson's relations

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Automatic reduction of elliptic integrals using Carlson's relations

In a series of papers, B. C. Carlson produced tables of elliptic integrals, evaluating them in terms of easily computed symmetrical functions, using a group of multivariate recurrence relations. These relations are, however, cumbersome to use by hand and, in the absence of a specific reductive algorithm, difficult to use with computer algebra. This paper presents such an algorithm, guaranteed t...

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Three 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...

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Reduction of Elliptic Integrals to Legendre Normal Form

It is well known that any elliptic integral can be transformed into a linear combination of elementary functions and Legendre’s three Elliptic functions. Methods for transforming these integrals to the Legendre form are described in numerous papers and textbooks. However, when it comes to actually designing and implementing such a reduction algorithm the existing methods require significant mod...

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Integrals 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: Mathematics of Computation

سال: 2001

ISSN: 0025-5718

DOI: 10.1090/s0025-5718-01-01333-3