On high precision methods for computing integrals involving Bessel functions

Author:
Bruno Gabutti

Journal:
Math. Comp. **33** (1979), 1049-1057

MSC:
Primary 65D30

MathSciNet review:
528057

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The technique of Bakhvalov and Vasil'eva for evaluating Fourier integrals is generalized to integrals involving exponential and Bessel functions.

**[1]**N. S. BAKHVALOV & L. G. VASIL'EVA, "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.**[2]**J. Balázs and P. Turán,*Notes on interpolation. IX (Approximate representation of Fourier-transform)*, Acta Math. Acad. Sci. Hungar.**16**(1965), 215–220. MR**0174907****[3]**W. Barrett,*Convergence properties of Gaussian quadrature formulae*, Comput. J.**3**(1960/1961), 272–277. MR**0128073****[4]**C. W. Clenshaw and A. R. Curtis,*A method for numerical integration on an automatic computer*, Numer. Math.**2**(1960), 197–205. MR**0117885****[5]**R. J. Glauber,*High-energy collision theory*, Lectures in theoretical physics, Vol. I. Lectures delivered at the Summer Institute for Theoretical Physics, University of Colorado, Boulder, 1958 (edited by W. E. Brittin and L. G. Dunham), Interscience Publishers, New York-London, 1959, pp. 315–414. MR**0107488****[6]**I. S. GRADSHTEYN & I. M. RYZHIK,*Table of Integral Series and Products*, Academic Press, New York, 1965.**[7]**Peter Linz,*A method for computing Bessel function integrals*, Math. Comp.**26**(1972), 509–513. MR**0303687**, 10.1090/S0025-5718-1972-0303687-8**[8]**I. M. Longman,*Note on a method for computing infinite integrals of oscillatory functions*, Proc. Cambridge Philos. Soc.**52**(1956), 764–768. MR**0082193****[9]**J. N. Lyness,*Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature*, Math. Comp.**25**(1971), 87–104. MR**0290020**, 10.1090/S0025-5718-1971-0290020-2**[10]**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. 1, 41–52. MR**0433932****[11]**R. PIESSENS & A. HAEGEMANS,"Numerical calculation of Fourier transform integrals,"*Electron. Lett.*, v. 9, 1973, pp. 108-109.**[12]**N. M. Steen, G. D. Byrne, and E. M. Gelbard,*Gaussian quadratures for the integrals ₀^{∞}𝑒𝑥𝑝(-𝑥²)𝑓(𝑥)𝑑𝑥 and ₀^{𝑏}𝑒𝑥𝑝(-𝑥²)𝑓(𝑥)𝑑𝑥*, Math. Comp.**23**(1969), 661–671. MR**0247744**, 10.1090/S0025-5718-1969-0247744-3

Retrieve articles in *Mathematics of Computation*
with MSC:
65D30

Retrieve articles in all journals with MSC: 65D30

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0528057-5

Article copyright:
© Copyright 1979
American Mathematical Society