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# Asymptotic Expansions of Integrals of Two Bessel Functions

DOI link for Asymptotic Expansions of Integrals of Two Bessel Functions

Asymptotic Expansions of Integrals of Two Bessel Functions book

# Asymptotic Expansions of Integrals of Two Bessel Functions

DOI link for Asymptotic Expansions of Integrals of Two Bessel Functions

Asymptotic Expansions of Integrals of Two Bessel Functions book

## ABSTRACT

A number of problems in applied mathematics and physics lead to results represented by definite integrals containing products of special functions, such as Bessel functions, whose argument involves a parameter of certain physical content. Asymptotic behavior of the integrals for large positive values of the parameter is usually of particular interest in these problems. However, the evaluation of the integrals in this limit is, as a rule, not a trivial task. Direct numerical methods for accurate estimations of such integrals can, at 724best, provide sets of numbers and are of little use when the parameter is large enough. Infinite series representations of the integrals in ascending powers of the parameter also are of little value since poor convergence means that many terms are required to attain the necessary accuracy. In general, these series are not readily transformable into representative asymptotic series in inverse powers of the large parameter. Thus, direct asymptotic expansions of the integrals are required to obtain convenient analytic expressions that are useful for large values of the parameter.