EXPLICIT EXPRESSIONS FOR CERTAIN INDEFINITE INTEGRALS CONTAINING THE PRODUCT OF 2 BESSEL-FUNCTIONS OR THE SQUARE OF A LEGENDRE FUNCTION

The two indefinite integrals integral x(l)Zmu(x)ZnuBARdx and integral x(l)[P(nu)(x)]2dx, where Z and ZBAR are arbitrary cylinder functions (i.e., any solutions of Bessel's differential equation) and P is a Legendre function (i.e., either the first or second solution of Legendre's differential equation) am evaluated explicitly for certain very general ranges of the parameters l, mu, nu, and x. (Here, l denotes an integer and mu, nu denote arbitrary numbers.) Many of the results presented here have not been previously tabulated. A new expression for the definite integral integral-1/-1 [P(nu)(x)]2dx which does not explicitly involve the trigamma function psi' is also given. This new series converges more rapidly than that which expresses this integral in terms of psi'. A representation of psi' which may be new is also presented.