The Bloch-Grüneisen integrals. Some analytic expressions
type: Item
instance of: scholarly article
title: The Bloch-Grüneisen integrals. Some analytic expressions
zbMATH Open document ID: 0961.33015
DOI: 10.1023/A:1019128506683
author: Stefan Paszkowski
published in: Numerical Algorithms
publication date: 2000-09-07T00:00:00Z
review text: The authors give analytic expressions of the Bloch-Grüneisen integrals \(I_n(x)\) [\textit{M. Deutsch}, J. Phys. A: Math. Gen. 20, L811--L813 (1987)] and of similar integrals \(K_n(x)\) defined by \[ I_n(x)= \int^x_0 {t^ne^t \over(e^t-1)^2} dt;\quad K_n(x)= \int^x_0 {t^ne^t\over e^{2t}-1} dt. \] The result include the power series expansion in terms of Bernoulli numbers and an expression as a finite sum of polylogarithms. The numerical accuracy of the formulas is discussed in detail.
Mathematics Subject Classification ID: 33E20
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33F05
zbMATH DE Number: 1355517
zbMATH Keywords: Bloch-Grüneisen integrals
zbMATH Keywords: Bernoulli numbers
zbMATH Keywords: polylogarithms
reviewed by: Daniel Duverney
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1355517