Weighted quadrature formulas  for semi-infinite range integrals

Gradimir V. Milovanović

doi:10.33993/jnaat441-1063

Authors

Gradimir V. Milovanović Serbian Academy of Sciences and Arts http://orcid.org/0000-0002-3255-8127

DOI:

https://doi.org/10.33993/jnaat441-1063

Keywords:

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

Abstract views: 454

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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References

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