000131566 001__ 131566 000131566 005__ 20241125101124.0 000131566 0247_ $$2doi$$a10.1007/s00009-023-02511-1 000131566 0248_ $$2sideral$$a136960 000131566 037__ $$aART-2023-136960 000131566 041__ $$aeng 000131566 100__ $$0(orcid)0000-0001-8331-5160$$aAdell, José A.$$uUniversidad de Zaragoza 000131566 245__ $$aSeries acceleration via negative binomial probabilities 000131566 260__ $$c2023 000131566 5060_ $$aAccess copy available to the general public$$fUnrestricted 000131566 5203_ $$aMany special functions and analytic constants allow for a probabilistic representation in terms of inverse moments of [0, 1]-valued random variables. Under this assumption, we give fast computations of them with an explicit upper bound for the remainder term. One of the main features of the method is that the coefficients of the main term of the approximation always contain negative binomial probabilities which, in turn, can be precomputed and stored. Applications to the arctangent function, Dirichlet functions and their nth derivatives, and the Catalan, Gompertz, and Stieltjes constants are provided. 000131566 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000131566 590__ $$a1.1$$b2023 000131566 592__ $$a0.604$$b2023 000131566 591__ $$aMATHEMATICS$$b98 / 490 = 0.2$$c2023$$dQ1$$eT1 000131566 593__ $$aMathematics (miscellaneous)$$c2023$$dQ2 000131566 591__ $$aMATHEMATICS, APPLIED$$b163 / 332 = 0.491$$c2023$$dQ2$$eT2 000131566 594__ $$a1.8$$b2023 000131566 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000131566 7102_ $$12007$$2265$$aUniversidad de Zaragoza$$bDpto. Métodos Estadísticos$$cÁrea Estadís. Investig. Opera. 000131566 773__ $$g20, 317 (2023), 1-14$$pMediterranean Journal of Mathematics$$tMediterranean Journal of Mathematics$$x1660-5446 000131566 8564_ $$s373619$$uhttps://zaguan.unizar.es/record/131566/files/texto_completo.pdf$$yVersión publicada 000131566 8564_ $$s1199799$$uhttps://zaguan.unizar.es/record/131566/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000131566 909CO $$ooai:zaguan.unizar.es:131566$$particulos$$pdriver 000131566 951__ $$a2024-11-22-11:57:15 000131566 980__ $$aARTICLE