Series acceleration via negative binomial probabilities (Q6141227)

The author gives a new method close to the linear acceleration methods for alternating series. Such a method is based on the fact that many special functions and analytic constants allow for a probabilistic representation in terms of certain expressions. Applications to the arctangent function, Dirichlet functions and their $n$th derivatives, and the Catalan, Gompertz, and Stieltjes constants are provided.