Weber and Beltrami integrals of squared spherical Bessel functions: finite series evaluation and high-index asymptotics. (English) Zbl 1301.33027

Tomaschitz, Roman

Math. Methods Appl. Sci. 37, No. 9, 1249-1272 (2014).

The paper is devoted to the Weber integrals \[ E_\mu(n,p;a):= \int_0^{+\infty} k^{2+\mu} e^{-ak^2} j_n^2(pk) dk \] and the Beltrami integrals \[ H_\mu(n,p;b):= \int_0^{+\infty} k^{2+\mu} e^{-bk} j_n^2(pk) dk, \] where \(j_n\) denotes the spherical Bessel function. Finite series expansions of \(E_\mu(n,p;a)\) and \(H_\mu(n,p;b)\) are obtained and their high-index asymptotics are studied.

Reviewer: Allal Ghanmi (Rabat)

MSC:

33E20	Other functions defined by series and integrals
33F05	Numerical approximation and evaluation of special functions

Keywords:

spherical Bessel function; Weber integral; Beltrami integral; Debye expansion; Airy approximation

Software:

DLMF

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