Series representations of the Volterra function and the Fransén–Robinson constant

López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo

Publication:
Series representations of the Volterra function and the Fransén–Robinson constant

dc.contributor.author	López García, José Luis
dc.contributor.author	Pagola Martínez, Pedro Jesús
dc.contributor.author	Palacios Herrero, Pablo
dc.contributor.department	Estatistika, Informatika eta Matematika	eu
dc.contributor.department	Institute for Advanced Materials and Mathematics - INAMAT2	en
dc.contributor.department	Estadística, Informática y Matemáticas	es_ES
dc.contributor.funder	Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa	es
dc.date.accessioned	2022-01-21T09:16:26Z
dc.date.available	2023-12-01T00:00:13Z
dc.date.issued	2021
dc.description.abstract	The Volterra function μ(t,β,α) was introduced by Vito Volterra in 1916 as the solution to certain integral equations with a logarithmic kernel. Despite the large number of applications of the Volterra function, the only known analytic representations of this function are given in terms of integrals. In this paper we derive several convergent expansion of μ(t,β,α) in terms of incomplete gamma functions. These expansions may be used to implement numerical evaluation techniques for this function. As a particular application, we derive a numerical series representation of the Fransén–Robinson constant F := µ(1, 1, 0) = R ∞ 0 1 Γ(x) dx. Some numerical examples illustrate the accuracy of the approximations	en
dc.description.sponsorship	This research was supported by the Ministerio de Economía y Competitividad (MTM2017-83490-P) and the Universidad Pública de Navarra, Spain.	en
dc.embargo.lift	2023-12-01
dc.embargo.terms	2023-12-01
dc.format.extent	14 p.
dc.format.mimetype	application/pdf	en
dc.identifier.doi	10.1016/j.jat.2021.105641
dc.identifier.issn	0021-9045
dc.identifier.uri	https://academica-e.unavarra.es/handle/2454/41872
dc.language.iso	eng	en
dc.publisher	Elsevier	en
dc.relation.ispartof	Journal of Approximation Theory, 272 (2021) 105641	en
dc.relation.projectID	info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83490-P/ES/	en
dc.relation.publisherversion	https://doi.org/10.1016/j.jat.2021.105641
dc.rights	© 2021 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0	en
dc.rights.accessRights	info:eu-repo/semantics/openAccess	en
dc.rights.accessRights	Acceso abierto / Sarbide irekia	es
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject	Convergent series representation	en
dc.subject	Fransén-Robinson constant	en
dc.subject	Special functions	en
dc.subject	Volterra function	en
dc.title	Series representations of the Volterra function and the Fransén–Robinson constant	en
dc.type	info:eu-repo/semantics/article	en
dc.type	Artículo / Artikulua	es
dc.type.version	info:eu-repo/semantics/acceptedVersion	en
dc.type.version	Versión aceptada / Onetsi den bertsioa	es
dspace.entity.type	Publication
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