000062005 001__ 62005 000062005 005__ 20200221144221.0 000062005 0247_ $$2doi$$a10.1007/s00009-016-0792-7 000062005 0248_ $$2sideral$$a96252 000062005 037__ $$aART-2016-96252 000062005 041__ $$aeng 000062005 100__ $$0(orcid)0000-0001-8331-5160$$aAdell, J.A.$$uUniversidad de Zaragoza 000062005 245__ $$aAcceleration Methods for Series: A Probabilistic Perspective 000062005 260__ $$c2016 000062005 5060_ $$aAccess copy available to the general public$$fUnrestricted 000062005 5203_ $$aWe introduce a probabilistic perspective to the problem of accelerating the convergence of a wide class of series, paying special attention to the computation of the coefficients, preferably in a recursive way. This approach is mainly based on a differentiation formula for the negative binomial process which extends the classical Euler’s transformation. We illustrate the method by providing fast computations of the logarithm and the alternating zeta functions, as well as various real constants expressed as sums of series, such as Catalan, Stieltjes, and Euler–Mascheroni constants. 000062005 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E64$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2015-67006-P 000062005 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000062005 590__ $$a0.868$$b2016 000062005 591__ $$aMATHEMATICS$$b83 / 310 = 0.268$$c2016$$dQ2$$eT1 000062005 591__ $$aMATHEMATICS, APPLIED$$b138 / 255 = 0.541$$c2016$$dQ3$$eT2 000062005 592__ $$a0.655$$b2016 000062005 593__ $$aMathematics (miscellaneous)$$c2016$$dQ2 000062005 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000062005 700__ $$0(orcid)0000-0001-6555-4432$$aLekuona, A.$$uUniversidad de Zaragoza 000062005 7102_ $$12007$$2265$$aUniversidad de Zaragoza$$bDpto. Métodos Estadísticos$$cÁrea Estadís. Investig. Opera. 000062005 773__ $$g13, 6 (2016), 5063-5076$$pMediterranean Journal of Mathematics$$tMediterranean Journal of Mathematics$$x1660-5446 000062005 8564_ $$s294043$$uhttps://zaguan.unizar.es/record/62005/files/texto_completo.pdf$$yPostprint 000062005 8564_ $$s39175$$uhttps://zaguan.unizar.es/record/62005/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000062005 909CO $$ooai:zaguan.unizar.es:62005$$particulos$$pdriver 000062005 951__ $$a2020-02-21-13:15:09 000062005 980__ $$aARTICLE