A general quadrature formula using zeros of spherical Bessel functions as nodes

• Published in: ESAIM: Mathematical Modelling and Numerical Analysis Vol. 33; no. 5; pp. 879 - 893
• Main Authors: Ben Ghanem, Riadh, Frappier, Clément
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.09.1999
• Subjects: 30D10; 33C10; 41A55; 65D32; Approximations and expansions; Bessel functions; Cauchy; Exact sciences and technology; Functions of a complex variable; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Quadrature; residue; Sciences and techniques of general use; Special functions; Bessel function; Integration; Cauchy integrability; Cauchy integral formula; Lebesgue integrability; Cauchy existence; Quadrature formula; Entire function; Exponential function
• ISSN: 0764-583X; 1290-3841
• DOI: 10.1051/m2an:1999124

We obtain, for entire functions of exponential type satisfying certain integrability conditions, a quadrature formula using the zeros of spherical Bessel functions as nodes. We deduce from this quadrature formula a result of Olivier and Rahman, which refines itself a formula of Boas. Nous obtenons, pour les fonctions entières de type exponentiel satisfaisant certaines conditions d'intégrabilité, une formule de quadrature utilisant les zéros des fonctions de Bessel sphériques comme nœuds. Nous déduisons de cette formule un résultat de Olivier et Rahman, lequel est lui-même un raffinement d'une formule préalablement obtenue par Boas.