Publication:
An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions

Date

2022

Director

Publisher

Springer
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión publicada / Argitaratu den bertsioa

Project identifier

AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/RTI2018-095499-B-C31/ES/recolecta

Abstract

We derive new convergent expansions of the symmetric standard elliptic integral RD(x,y,z), for x,y,z∈C∖(−∞,0], in terms of elementary functions. The expansions hold uniformly for large and small values of one of the three variables x, y or z (with the other two fixed). We proceed by considering a more general parametric integral from which RD(x,y,z) is a particular case. It turns out that this parametric integral is an integral representation of the Appell function F1(a;b,c;a+1;x,y). Therefore, as a byproduct, we deduce convergent expansions of F1(a;b,c;a+1;x,y). We also compute error bounds at any order of the approximation. Some numerical examples show the accuracy of the expansions and their uniform features.

Description

Keywords

Symmetric standard elliptic integrals, Appell function, Convergent expansions, Uniform expansions, Error bounds

Department

Estatistika, Informatika eta Matematika / Institute for Advanced Materials and Mathematics - INAMAT2 / Estadística, Informática y Matemáticas

Faculty/School

Degree

Doctorate program

item.page.cita

Bujanda, B., López, J.L., Pagola, P.J. et al. An Analytic Representation of the Second Symmetric Standard Elliptic Integral in Terms of Elementary Functions. Results Math 77, 171 (2022). https://doi.org/10.1007/s00025-022-01707-3

item.page.rights

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