The summation of power series and Fourier series
type: Item
instance of: scholarly article
title: The summation of power series and Fourier series
zbMATH Open document ID: 0574.65003
DOI: 10.1016/0377-0427(85)90038-X
author: I. M. Longman
published in: Journal of Computational and Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: For evaluating a sum of a power series \(s(x)=u_ 1-u_ 2x+u_ 3x^ 2- ... \), of a variable x, the coefficients \(u_ k\) are revealed as the moments \(u_ k=\int^{\infty}_{0}u^{k-1}f(u)du\) of the function f(u). In this paper, the f(u) is determined by the inversion of the two- sided Laplace transform of the \(u_ k\). Thus, the summation results in numerical calculation of the Stieltjes integral \(I(x)=\int^{\infty}_{0}f(u)/(1+ux)du.\)
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 40A25
Mathematics Subject Classification ID: 40C10
Mathematics Subject Classification ID: 42A24
Mathematics Subject Classification ID: 30B10
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 3917524
zbMATH Keywords: summation of power series
zbMATH Keywords: summation of Fourier series
zbMATH Keywords: inverse of the two-sided Laplace transform
zbMATH Keywords: Mellin transform
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3917524