Asymptotic and factorial expansions of Euler series truncation errors via exponential polynomials

Authors:
Riccardo Borghi
Affiliations:
Dipartimento di Elettronica Applicata, Universití degli Studi "Roma Tre", Rome, Italy
Venue:
Applied Numerical Mathematics
Year:
2010

Citing 2
Cited 1

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Asymptotic analysis of the Bell polynomials by the ray method

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Acceleration of generalized hypergeometric functions through precise remainder asymptotics

Numerical Algorithms

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Abstract

A detailed analysis of the remainder obtained by truncating the Euler series up to the nth-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse powers and in inverse rising factorials of n, are obtained. It is found that the corresponding expanding coefficients are expressed, in closed form, in terms of exponential polynomials, well known in combinatorics, and in terms of associated Laguerre polynomials, respectively. A study of the divergence and/or of the convergence of the above expansions is also carried out for positive values of the Euler series argument.