Indefinite integrals involving Bessel functions

Expressio ns are derived for the indefinite integral s, J,!( r ) Co(ar )dr Irf(r ) q (ar )elr I ,!(r) C,,(ar ) Co(f3r)elr a "" f3 y,!(r) Co(ar ) Z,,(Ar )dr whe re Co(ar) are ze ro order Bessel fun c tions, ZoO...,.) are zero ord e r modifi ed Bessel fun ction s a nd f( r ) is a polyn om ial in r.-In general, th e expressions given for the integrals are give n in te rm s of presc rib ed fun c tion s of the Bessel fun c ti ons, and th e coefficient s of these fun c tions are determin ed from a finite series, th e te rm s of whic h a re found from rec urre nce relati onships that involve only the polynomial fIr) _ Coeffic ie nts of th e te rm s of the fin ite seri es are give n in tabular form for up to an ele ve nth degree polynomial.