A quadrature formula with zeros of Bessel functions as nodes

Grozev, Georgi R.; Rahman, Qazi I.

doi:10.1090/S0025-5718-1995-1277767-2

A quadrature formula with zeros of Bessel functions as nodes
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by Georgi R. Grozev and Qazi I. Rahman PDF

Math. Comp. 64 (1995), 715-725 Request permission

Abstract:

A quadrature formula for entire functions of exponential type wherein the nodes are the zeros of the Bessel function of the first kind was recently obtained by C. Frappier and P. Olivier. Here the condition imposed on the function is relaxed. Some applications of the formula are also given.

References

R. P. Boas Jr., Inequalities between series and integrals involving entire functions, J. Indian Math. Soc. (N.S.) 16 (1952), 127–135. MR 52511
Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
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
A. R. Harvey, The mean of a function of exponential type, Amer. J. Math. 70 (1948), 181–202. MR 24981, DOI 10.2307/2371945
M. Plancherel and G. Pólya, Fonctions entières et intégrales de fourier multiples, Comment. Math. Helv. 10 (1937), no. 1, 110–163 (French). MR 1509570, DOI 10.1007/BF01214286
G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469, DOI 10.1017/CBO9780511608759