On high precision methods for computing integrals involving Bessel functions
HTML articles powered by AMS MathViewer
- by Bruno Gabutti PDF
- Math. Comp. 33 (1979), 1049-1057 Request permission
Abstract:
The technique of Bakhvalov and Vasilโeva for evaluating Fourier integrals is generalized to integrals involving exponential and Bessel functions.References
-
N. S. BAKHVALOV & L. G. VASILโEVA, "Evaluation of the integrals of oscillating functions by interpolation at nodes of Gaussian quadratures," USSR Comp. Math. and Math. Phys., v. 8, 1968, pp. 241-249.
- J. Balรกzs and P. Turรกn, Notes on interpolation. IX (Approximate representation of Fourier-transform), Acta Math. Acad. Sci. Hungar. 16 (1965), 215โ220. MR 174907, DOI 10.1007/BF01886401
- W. Barrett, Convergence properties of Gaussian quadrature formulae, Comput. J. 3 (1960/61), 272โ277. MR 128073, DOI 10.1093/comjnl/3.4.272
- C. W. Clenshaw and A. R. Curtis, A method for numerical integration on an automatic computer, Numer. Math. 2 (1960), 197โ205. MR 117885, DOI 10.1007/BF01386223
- R. J. Glauber, High-energy collision theory, Lectures in theoretical physics, Vol. I., Interscience Publishers, New York-London, 1959, pp.ย 315โ414. Lectures delivered at the Summer Institute for Theoretical Physics, University of Colorado, Boulder, 1958 (edited by W. E. Brittin and L. G. Dunham). MR 0107488 I. S. GRADSHTEYN & I. M. RYZHIK, Table of Integral Series and Products, Academic Press, New York, 1965.
- Peter Linz, A method for computing Bessel function integrals, Math. Comp. 26 (1972), 509โ513. MR 303687, DOI 10.1090/S0025-5718-1972-0303687-8
- I. M. Longman, Note on a method for computing infinite integrals of oscillatory functions, Proc. Cambridge Philos. Soc. 52 (1956), 764โ768. MR 82193
- J. N. Lyness, Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature, Math. Comp. 25 (1971), 87โ104. MR 290020, DOI 10.1090/S0025-5718-1971-0290020-2
- T. N. L. Patterson, On high precision methods for the evaluation of Fourier integrals with finite and infinite limits, Numer. Math. 27 (1976/77), no.ย 1, 41โ52. MR 433932, DOI 10.1007/BF01399083 R. PIESSENS & A. HAEGEMANS,"Numerical calculation of Fourier transform integrals," Electron. Lett., v. 9, 1973, pp. 108-109.
- N. M. Steen, G. D. Byrne, and E. M. Gelbard, Gaussian quadratures for the integrals $_{0}^{\infty }\,\textrm {exp}(-x^{2})f(x)dx$ and $_{0}^{b}\,\textrm {exp}(-x^{2})f(x)dx$, Math. Comp. 23 (1969), 661โ671. MR 247744, DOI 10.1090/S0025-5718-1969-0247744-3
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 1049-1057
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1979-0528057-5
- MathSciNet review: 528057