THE EVALUATION OF SOME DEFINITE INTEGRALS INVOLVING BESSEL FUNCTIONS WHICH OCCUR IN HYDRODYNAMICS AND ELASTICITY,

The integrals I sub 1m, 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