Indefinite integrals involving Bessel functions

Abstract

Expressions are derived for the indefinite integrals: ∫ r f(r) Co(αr) dr, ∫ r f(r) Co^2(αr) dr, ∫ r f(r) Co(αr) Co(βr) dr, α ≠ β, ∫ r f(r) Co(αr ) Zo(λr) dr, where Co(αr) are zero order Bessel functions, Zo(λr) are zero order modified Bessel functions and f(r) is a polynomial in r. In general, the expressions given for the integrals are given in te rms of prescribed functions of the Bessel functions, and the coefficients of these functions are determined from a finite series, the terms of which are found from recurrence relationships that involve only the polynomial f(r). Coefficients of the terms of the finite series are given in tabular form for up to an eleventh degree polynomial.