Abstract
AbstractMany 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.
Funder
Diputación General de Aragón
Universidad de Zaragoza
Publisher
Springer Science and Business Media LLC
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