Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type

D. V. Gorbachev   ; V. I. Ivanov

Sbornik. Mathematics, Tome 206 (2015) no. 8, pp. 1087-1122

Résumé

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles.

Détail

Keywords: entire function of exponential type, Jacobi functions and polynomials.
Mots-clés : Gauss and Markov quadrature formulae, Sturm-Liouville problem, Jacobi transform

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