000161074 001__ 161074 000161074 005__ 20251017144618.0 000161074 0247_ $$2doi$$a10.1007/s11075-025-02113-w 000161074 0248_ $$2sideral$$a144283 000161074 037__ $$aART-2025-144283 000161074 041__ $$aeng 000161074 100__ $$aLópez, José L. 000161074 245__ $$aNew analytic representations of the Lerch transcendent 000161074 260__ $$c2025 000161074 5060_ $$aAccess copy available to the general public$$fUnrestricted 000161074 5203_ $$aWe consider an integral representation of the Lerch transcendent function (z, s, a) of the form (z, s, a) = 1 0h(t, z)g(t, s, a)dt, and two different analytical methods for the approximation of this integral transform to obtain new convergent expansions of the Lerch transcendent in the variable z. The first method uses multi-point Taylor expansions of h(t, z) at certain appropriately selected base points that provides convergent expansions of the Lerch transcendent in terms of elementary functions of z uniformly valid in compact sets of the complex z−plane. The second method expands g(t, s, a) in a Taylor series at a selected point in [0, 1] giving a uniform convergent expansion of (z, s, a) in terms of elementary functions of z valid in a large unbounded region of the complex plane. We provide explicit and/or recursive algorithms for the computation of the coefficients of the expansions. Numerical experiments illustrate the accuracy of the new approximations. 000161074 536__ $$9info:eu-repo/grantAgreement/ES/MCINN/PID2022-136441NB-I00 000161074 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000161074 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000161074 700__ $$0(orcid)0000-0002-8021-2745$$aPérez Sinusía, Ester$$uUniversidad de Zaragoza 000161074 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000161074 773__ $$g(2025), [22 pp.]$$pNumer. algorithms$$tNUMERICAL ALGORITHMS$$x1017-1398 000161074 8564_ $$s1042939$$uhttps://zaguan.unizar.es/record/161074/files/texto_completo.pdf$$yVersión publicada 000161074 8564_ $$s1110456$$uhttps://zaguan.unizar.es/record/161074/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000161074 909CO $$ooai:zaguan.unizar.es:161074$$particulos$$pdriver 000161074 951__ $$a2025-10-17-14:20:32 000161074 980__ $$aARTICLE