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

Journal Article · Mon Aug 31 00:00:00 EDT 2015 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2015V206N08ABEH004490· OSTI ID:22590451

Gorbachev, D V; Ivanov, V I ^[1]

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1. Tula State University, Tula (Russian Federation)

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.

• OSTI ID: 22590451
• Journal Information: Sbornik. Mathematics, Vol. 206, Issue 8; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BESSEL FUNCTIONS
EIGENFUNCTIONS
INTEGRAL TRANSFORMATIONS
INTEGRALS
MARKOV PROCESS
POLYNOMIALS
QUADRATURES
STURM-LIOUVILLE EQUATION