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López García, José Luis

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https://academica-e.unavarra.es/handle/2454/49435

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López García

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José Luis

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-6050-9015

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2369

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Subject: Convergent expansions × Subject: Appell function ×

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    PublicationOpen Access
    An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions
    (Springer, 2022) Bujanda Cirauqui, Blanca; López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
    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.