Series acceleration via negative binomial probabilities

Adell, José A. (Universidad de Zaragoza)

Resumen: Many 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.

Idioma: Inglés

DOI: 10.1007/s00009-023-02511-1

Año: 2023

Publicado en: Mediterranean Journal of Mathematics 20, 317 (2023), 1-14
ISSN: 1660-5446

Factor impacto JCR: 1.1 (2023)

Categ. JCR: MATHEMATICS rank: 98 / 490 = 0.2 (2023) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 163 / 332 = 0.491 (2023) - Q2 - T2

Factor impacto CITESCORE: 1.8 - Mathematics (all) (Q2)

Factor impacto SCIMAGO: 0.604 - Mathematics (miscellaneous) (Q2)

Tipo y forma: Article (Published version)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)