论文信息 - Evaluating infinite integrals involving products of Bessel functions of arbitrary order

Evaluating infinite integrals involving products of Bessel functions of arbitrary order

The difficulties involved with evaluating infinite integrals involving products of Bessel functions are considered, and a method for evaluating these integrals is outlined. The method makes use of extrapolation on a sequence of partial sums, and requires rewriting the product of Bessel functions as the sum of two more well-behaved functions. Numerical results are presented to demonstrate the efficiency of this method, where it is shown to be significantly superior to standard infinite integration routines.

S. K. Lucas | S. Lucas

[1] Peter Linz,et al. A note on the computation of integrals involving products of trigonometric and Bessel functions , 1973 .

[2] Avram Sidi,et al. A user-friendly extrapolation method for oscillatory infinite integrals , 1988 .

[3] H. M. McConnell,et al. Hydrodynamics of quantized shape transitions of lipid domains , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[4] R. Wong. Asymptotic expansion of $\int\sp {\pi/2}\sb 0J\sp 2\sb \nu(\lambda\,{\rm cos}\,\theta)\,d\theta$ , 1988 .

[5] J. N. Lyness. Integrating some infinite oscillating tails , 1985 .

[6] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[7] Howard A. Stone,et al. Motion of a rigid particle in a rotating viscous flow: an integral equation approach , 1994, Journal of Fluid Mechanics.

[8] Anthony M. J. Davis. Drag modifications for a sphere in a rotational motion at small, non-zero Reynolds and Taylor numbers : wake interference and possibly Coriolis effects , 1992 .

[9] M. Tezer,et al. On the numerical evaluation of an oscillating infinite series , 1989 .

[10] R. Wong. Asymptotic expansion of ∫^{/2}₀²_{}() , 1988 .

[11] Howard A. Stone,et al. Evaluating innite integrals involving Bessel functions of arbitrary order , 1995 .