Quadrature formulae using zeros of Bessel functions as nodes

Ben Ghanem, Riadh

doi:10.1090/S0025-5718-98-00882-5

Quadrature formulae using zeros of Bessel functions as nodes
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Math. Comp. 67 (1998), 323-336 Request permission

Abstract:

A gaussian type quadrature formula, where the nodes are the zeros of Bessel functions of the first kind of order $\alpha$ ($\Re (\alpha ) > -1$), was recently proved for entire functions of exponential type. Here we relax the restriction on $\alpha$ as well as on the function. Some applications are also given.

References

Riadh Ben Ghanem and Clément Frappier, Spherical Bessel functions and explicit quadrature formula, Math. Comp. 66 (1997), no. 217, 289–296. MR 1372005, DOI 10.1090/S0025-5718-97-00794-1
P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
R. P. Boas Jr., Summation formulas and band-limited signals, Tohoku Math. J. (2) 24 (1972), 121–125. MR 330915, DOI 10.2748/tmj/1178241524
Clément Frappier and Patrick Olivier, A quadrature formula involving zeros of Bessel functions, Math. Comp. 60 (1993), no. 201, 303–316. MR 1149290, DOI 10.1090/S0025-5718-1993-1149290-5
C. Frappier and Q. I. Rahman, Une formule de quadrature pour les fonctions entières de type exponentiel, Ann. Sci. Math. Québec 10 (1986), no. 1, 17–26 (French). MR 841119
R. Gervais, Q. I. Rahman, and G. Schmeisser, Representation and approximation of functions via $(0,2)$-interpolation, J. Approx. Theory 50 (1987), no. 2, 89–110. MR 888292, DOI 10.1016/0021-9045(87)90001-3
Georgi R. Grozev and Qazi I. Rahman, A quadrature formula with zeros of Bessel functions as nodes, Math. Comp. 64 (1995), no. 210, 715–725. MR 1277767, DOI 10.1090/S0025-5718-1995-1277767-2
Qazi I. Rahman and Gerhard Schmeisser, Quadrature formulae and functions of exponential type, Math. Comp. 54 (1990), no. 189, 245–270. MR 990602, DOI 10.1090/S0025-5718-1990-0990602-8
Walter Rudin, Real and complex analysis, 2nd ed., McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1974. MR 0344043
G. N. Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambridge Univ. Press, Cambridge, 1966.