A quadrature formula involving zeros of Bessel functions

Author:

Frappier Clément,Olivier Patrick

Abstract

An exact quadrature formula for entire functions of exponential type is obtained. The nodes of the formula are zeros of the Bessel function of the first kind of order α \alpha . It generalizes and refines a known quadrature formula related to the sampling theorem. The uniqueness of the nodes is studied.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference7 articles.

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2. Une formule de quadrature pour les fonctions entières de type exponentiel;Frappier, C.;Ann. Sci. Math. Qu\'{e}bec,1986

3. Representation and approximation of functions via (0,2)-interpolation;Gervais, R.;J. Approx. Theory,1987

4. Notes on special systems of orthogonal functions. IV. The orthogonal functions of Whittaker’s cardinal series;Hardy, G. H.;Proc. Cambridge Philos. Soc.,1941

5. An analogue of Turán’s quadrature formula;Rahman, Q. I.,1988

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