The evaluation of some definite integrals involving Bessel functions which occur in hydrodynamics and elasticity

Abstract

Abstract : The integrals I sub 1(m, nu) integral evaluated from 0 to infinity of -xt power of e J sub nu (yt) J sub nu (bt) m power of t dt and I sub 2 (m, nu) integral evaluated from 0 to infinity of -xt power of e J sub nu-1 (yt) J sub nu (bt) m1 power of t dt are considered, where x,y, and b are complex. Results are given for the evaluation of I sub 1 (m, nu) and I sub 2 (m, nu) in terms of associated Legendre functions of the second kind when m is greater than or equals 0 and nu is complex, and for the evaluation sub 1 (m,n) and I sub 2 (m,n) in terms of elliptic integrals when n greater than or equal to 0 is an integer. Recurrence relations are given for the calculation of I sub 1 (m,n) and I sub 2 (m,n) when I sub 1 (m,n) is known for certain values of m and n. (Author)