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Resumen: We 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.
Idioma: Inglés
DOI: 10.1007/s00009-016-0792-7
Año: 2016
Publicado en: Mediterranean Journal of Mathematics 13, 6 (2016), 5063-5076
ISSN: 1660-5446
Factor impacto JCR: 0.868 (2016)
Categ. JCR: MATHEMATICS rank: 83 / 310 = 0.268 (2016) - Q2 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 138 / 255 = 0.541 (2016) - Q3 - T2
Factor impacto SCIMAGO: 0.655 - Mathematics (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E64
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2015-67006-P
Tipo y forma: Artículo (PostPrint)
Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)

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