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: 458

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 $2 n - 1$ . In particular, quadrature formulas with respect to the weight function $x \mapsto w (x) = x^{β} \log^{m} x$ ( $0 \leq β < 1$ , $m \in N_{0}$ ) are considered and several numerical examples are included.

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References

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