A method for computing Bessel function integrals

Author:
Peter Linz

Journal:
Math. Comp. **26** (1972), 509-513

MSC:
Primary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1972-0303687-8

MathSciNet review:
0303687

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Infinite integrals involving Bessel functions are recast, by means of an Abel transform, in terms of Fourier integrals. As there are many efficient numerical methods for computing Fourier integrals, this leads to a convenient way of approximating Bessel function integrals.

**[1]**Stephen M. Chase and Lloyd D. Fosdick,*An algorithm for Filon quadrature*, Comm. ACM**12**(1969), 453–457. MR**0279999**, https://doi.org/10.1145/363196.363209**[2]**W. W. Clendenin,*A method for numerical calculation of Fourier integrals*, Numer. Math.**8**(1966), 422–436. MR**0201097**, https://doi.org/10.1007/BF02166668**[3]**Philip J. Davis and Philip Rabinowitz,*Numerical integration*, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967. MR**0211604****[4]**A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi,*Tables of integral transforms. Vol. I*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954. Based, in part, on notes left by Harry Bateman. MR**0061695****[5]**L. N. G. Filon, ``On a quadrature formula for trigonometric integrals,''*Proc. Roy. Soc. Edinburgh*, v. 49, 1928, pp. 38-47.**[6]**I. M. Longman,*Tables for the rapid and accurate numerical evaluation of certain infinite integrals involving Bessel functions*, Math. Tables Aids Comput.**11**(1957), 166–180. MR**0091538**, https://doi.org/10.1090/S0025-5718-1957-0091538-0**[7]**J. N. Lyness,*The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula. I. Functions whose early derivatives are continuous*, Math. Comp.**24**(1970), 101–135. MR**0260230**, https://doi.org/10.1090/S0025-5718-1970-0260230-8**[8]**Ian N. Sneddon,*Boundary value problems in thermoelasticity*, Boundary problems in differential equations, Univ. of Wisconsin Press, Madison, 1960, pp. 231–241. MR**0112417****[9]**Ian N. Sneddon,*Mixed boundary value problems in potential theory*, North-Holland Publishing Co., Amsterdam; Interscience Publishers John Wiley & Sons, Inc., New York, 1966. MR**0216018****[10]**G. N. Watson,*A Treatise on the Theory of Bessel Functions*, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR**0010746****[11]**Andrew Young,*Approximate product-integration*, Proc. Roy. Soc. London Ser. A.**224**(1954), 552–561. MR**0063778**, https://doi.org/10.1098/rspa.1954.0179**[12]**An adaptive quadrature method based on Filon's method. A FORTRAN program of this algorithm is available from the author.

Retrieve articles in *Mathematics of Computation*
with MSC:
65D20

Retrieve articles in all journals with MSC: 65D20

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0303687-8

Keywords:
Bessel functions,
Fourier-Bessel coefficients,
Hankel transforms,
numerical integration

Article copyright:
© Copyright 1972
American Mathematical Society