Comments on “Asymptotic expansion of a Bessel function integral using hypergeometric functions” by L.J. Landau and N.J. Luswili

Abstract

In a recent paper Landau and Luswili ( J. Comput. Appl. Math. 132 (2001) 387) used generalized hypergeometric functions to obtain a complete asymptotic expansion for the integral ∫ 0 π / 2 J μ ( λ sin θ ) J ν ( λ sin θ ) d θ , where J μ is the μ th-order Bessel function of the first kind and λ is a large parameter tending to infinity. The purpose of this note is to point out that the same complete asymptotic expansion for this integral (as well as another one for a Hankel-type integral) has previously been obtained by Stoyanov et al. ( J. Comput. Appl. Math. 50 (1994) 533) by using the same method. In addition, an alternative, simpler representation of the algebraic series contribution to the asymptotic expansion is provided. A few errors are also corrected and additional relevant references indicated.