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

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: entire function of exponential type, Jacobi functions and polynomials.
Mots-clés : Gauss and Markov quadrature formulae, Sturm-Liouville problem, Jacobi transform 
@article{SM_2015_206_8_a2,
     author = {D. V. Gorbachev and V. I. Ivanov},
     title = {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 = {Sbornik. Mathematics},
     pages = {1087--1122},
     publisher = {mathdoc},
     volume = {206},
     number = {8},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_8_a2/}
}
TY  - JOUR
AU  - D. V. Gorbachev
AU  - V. I. Ivanov
TI  - 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
JO  - Sbornik. Mathematics
PY  - 2015
SP  - 1087
EP  - 1122
VL  - 206
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2015_206_8_a2/
LA  - en
ID  - SM_2015_206_8_a2
ER  - 
%0 Journal Article
%A D. V. Gorbachev
%A V. I. Ivanov
%T 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
%J Sbornik. Mathematics
%D 2015
%P 1087-1122
%V 206
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2015_206_8_a2/
%G en
%F SM_2015_206_8_a2
D. V. Gorbachev; V. I. Ivanov. 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. Sbornik. Mathematics, Tome 206 (2015) no. 8, pp. 1087-1122. http://geodesic.mathdoc.fr/item/SM_2015_206_8_a2/