Chebyshev coefficients for the Clausen function \(Cl_ 2(x)\)
type: Item
instance of: scholarly article
title: Chebyshev coefficients for the Clausen function \(Cl_ 2(x)\)
zbMATH Open document ID: 0853.65024
DOI: 10.1016/0377-0427(95)00150-6
author: K. S. Kölbig
published in: Journal of Computational and Applied Mathematics
publication date: 1997-01-05T00:00:00Z
review text: The Clausen function \(Cl_2(x)= - \int^x_0 \ln|2\sin (t/2)|dt\) is expanded in the forms \[ Cl_2(x)= \begin{cases} x- x\ln |x|+ \textstyle{{1\over 2}} x^3 \displaystyle{ \sum^\infty_{n= 0}} a_n T_{2n}(2x/\pi)\quad&\text{for }|x|\leq \pi/2\text{ and}\\ (\pi- x) \sum^\infty_{n= 0} b_n T_{2n}(2x/\pi)\quad&\text{for }\pi/2 < x\leq 3\pi/2.\end{cases} \] The numerical values of the coefficients \(a_n\), \(b_n\) (twenty digits) are given for evaluating the series.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33E20
zbMATH DE Number: 903556
zbMATH Keywords: dilogarithm
zbMATH Keywords: Clausen function
Wikidata QID: Q56018950
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00150-6
OpenAlex ID: W2021378606
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description: scientific article; zbMATH DE number 903556