Power series in the complementary modulus for the first and second complete elliptic integrals are deduced in terms of binomial series, by exploiting a suitable decomposition of the integration domain. This approach appears to be straightforward, with respect to the standard one. However, despite the procedure is simple, it needs some non-trivial results about binomial series proved in the appendix. Numerical performances of the expansions are also discussed and compared with existing alternative expansions.

Asymptotic expansions of the complete elliptic integrals about unitary modulus / Riccardi, Giorgio; Vellucci, Pierluigi; DE BERNARDIS, Enrico. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - ELETTRONICO. - 5:(2014), pp. 1-12. [10.1685/journal.caim.490]

Asymptotic expansions of the complete elliptic integrals about unitary modulus.

VELLUCCI, PIERLUIGI;DE BERNARDIS, ENRICO
2014

Abstract

Power series in the complementary modulus for the first and second complete elliptic integrals are deduced in terms of binomial series, by exploiting a suitable decomposition of the integration domain. This approach appears to be straightforward, with respect to the standard one. However, despite the procedure is simple, it needs some non-trivial results about binomial series proved in the appendix. Numerical performances of the expansions are also discussed and compared with existing alternative expansions.
complete elliptic integrals, asymptotic expansions, computation of special functions.
01 Pubblicazione su rivista::01a Articolo in rivista
Asymptotic expansions of the complete elliptic integrals about unitary modulus / Riccardi, Giorgio; Vellucci, Pierluigi; DE BERNARDIS, Enrico. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - ELETTRONICO. - 5:(2014), pp. 1-12. [10.1685/journal.caim.490]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/849056
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