Numerical calculation of the generalized sine and cosine integral.
type: Item
instance of: scholarly article
title: Numerical calculation of the generalized sine and cosine integral.
zbMATH Open document ID: 1037.65031
author: Klaus-Dieter Reinsch
author: U. Puschmann
author: Roland Bulirsch
published in: Rocky Mountain Journal of Mathematics
publication date: 2003-12-03T00:00:00Z
full work available at URL: CONT32-2.html
review text: This paper concerns the efficient calculation of \[ \text{Si}(x, a)= \int^x_0 t^{-a}\sin t\,dt,\quad 0< a< 2, \] and \[ \text{Ci}(x, a)= \int^x_0 t^{-a} \cos t\,dt,\quad 0< a< 1, \] investigated in detail by the reviewer [Acta Math. 85, 117--181 (1951; Zbl 0042.30304), Acta Math. 89, 107--131 (1953; Zbl 0050.07305)] suitable when a great number of function evaluations is needed as for aircraft simulation. The evaluation is based on (truncated) Chebyshev series for sine and cosine, first in the range \(0< x\leq\lambda\) and then for \(\lambda< x<\infty\) with \(\lambda\) suitably determined.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33B20
Mathematics Subject Classification ID: 33F05
zbMATH DE Number: 2012119
zbMATH Keywords: generalized sine and cosine integral
zbMATH Keywords: Chebyshev series
reviewed by: Erwin O. Kreyszig
describes a project that uses: Mathematica
MaRDI profile type: Publication
OpenAlex ID: W2007151172
cites work: Q5558293
cites work: Numerical calculation of the sine, cosine and Fresnel integrals
cites work: Über den allgemeinen Integralsinus \(Si(z,\alpha)\)
cites work: Chebyshew expansions for Fresnel integrals
cites work: Anschauliches zur Gibbschen Erscheinung und zur Annäherung durch arithmetische Mittel
DOI: 10.1216/RMJM/1030539698
description: scientific article; zbMATH DE number 2012119