Weighted quadrature formulas for semi-infinite range integrals

Keywords: Gaussian quadrature rules, nodes, Christoffel numbers, non-exponentially decreasing integrands.

Abstract

Weighted quadrature formulas on the half line \((a,+\infty)\), \(a>0\), for non-exponentially decreasing integrands are developed. Such \(n\)-point quadrature rules are exact for all functions of the form \(x\mapsto x^{-2}P(x^{-1})\), where \(P\) is an arbitrary algebraic polynomial of degree at most \(2n-1\). In particular, quadrature formulas with respect to the weight function \(x\mapsto w(x)=x^\beta\log^m x\) (\(0\le \beta<1\), \(m\in \mathbb{N}_0\)) are considered and several numerical examples are included.

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Published
2015-12-18
How to Cite
Milovanović, G. V. (2015). Weighted quadrature formulas for semi-infinite range integrals. J. Numer. Anal. Approx. Theory, 44(1), 69-80. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2015-vol44-no1-art6
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Articles