A note on the asymptotic expansion of the Lerch’s transcendent

Cai, Xing Shi; López García, José Luis

Publication:
A note on the asymptotic expansion of the Lerch’s transcendent

dc.contributor.author	Cai, Xing Shi
dc.contributor.author	López García, José Luis
dc.contributor.department	Ingeniería Matemática e Informática	es_ES
dc.contributor.department	Matematika eta Informatika Ingeniaritza	eu
dc.date.accessioned	2019-06-20T08:02:55Z
dc.date.available	2019-09-10T23:00:14Z
dc.date.issued	2018
dc.description	This is an accepted manuscript of an article published by Taylor & Francis in Integral Transforms and Special Functions on 10 Jun 2019, available online: https://doi.org/10.1080/10652469.2019.1627530	en
dc.description.abstract	In Ferreira and López [Asymptotic expansions of the Hurwitz–Lerch zeta function. J Math Anal Appl. 2004;298(1):210–224], the authors derived an asymptotic expansion of the Lerch's transcendent Φ(z,s,a) for large \|a\|, valid for Ra>0, Rs>0 and z∈C∖[1,∞). In this paper, we study the special case z≥1 not covered in Ferreira and López [Asymptotic expansions of the Hurwitz–Lerch zeta function. J Math Anal Appl. 2004;298(1):210–224], deriving a complete asymptotic expansion of the Lerch's transcendent Φ(z,s,a) for z>1 and Rs>0 as Ra goes to infinity. We also show that when a is a positive integer, this expansion is convergent for Rz≥1. As a corollary, we get a full asymptotic expansion for the sum ∑mn=1zn/ns for fixed z>1 as m→∞. Some numerical results show the accuracy of the approximation.	en
dc.description.sponsorship	This work is supported by the Knut and Alice Wallenberg Foundation and the Ministerio de Economía y Competitividad of the spanish government (MTM2017-83490-P).	en
dc.embargo.lift	2019-09-10
dc.embargo.terms	2019-09-10
dc.format.extent	12 p.
dc.format.mimetype	application/pdf	en
dc.identifier.doi	10.1080/10652469.2019.1627530
dc.identifier.issn	1065-2469 (Print)
dc.identifier.issn	1476-8291 (Electronic)
dc.identifier.uri	https://academica-e.unavarra.es/handle/2454/33465
dc.language.iso	eng	en
dc.publisher	Taylor & Francis	en
dc.relation.ispartof	Integral Transforms and Special Functions 2019, vol. 30, no. 10, 844–855	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/10.1080/10652469.2019.1627530
dc.rights	© 2019 Informa UK Limited, trading as Taylor & Francis Group	en
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.subject	Hurwitz–Lerch zeta function	en
dc.subject	Asymptotic expansion	en
dc.subject	Special functions	en
dc.title	A note on the asymptotic expansion of the Lerch’s transcendent	en
dc.type	info:eu-repo/semantics/article
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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