Uniform approximations of the first symmetric elliptic integral in terms of elementary functions
Fecha
2022Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Identificador del proyecto
Impacto
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10.1007/s13398-021-01151-y
Resumen
We consider the standard symmetric elliptic integral RF(x, y, z) for complex x, y, z. We derive convergent expansions of RF(x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y or z in closed subsets (possibly unbounded) of C\ (−∞, 0]. The expansions are accompanied by error bounds. The accuracy of the expansions and their uniform features are illustra ...
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We consider the standard symmetric elliptic integral RF(x, y, z) for complex x, y, z. We derive convergent expansions of RF(x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y or z in closed subsets (possibly unbounded) of C\ (−∞, 0]. The expansions are accompanied by error bounds. The accuracy of the expansions and their uniform features are illustrated by means of some numerical examples. [--]
Materias
Convergent expansions,
Error bounds,
Symmetric standard elliptic integrals,
Uniform expansions
Editor
Springer
Publicado en
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 116 (1)
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
The financial support of the following entities is acknowledged: Ministerio de Economía y Competitividad, project MTM2017-83490-P; Ministerio de Ciencia, Innovación y Universidades, research grant RTI2018-095499-B-C31 IoTrain; Gobierno de Navarra, Grant 0011-1365-2019-000083 - SIAGUS; the European Union-European Regional Development Fund ERDF-FEDER.