POSITIVITY OF INTEGRALS OF BESSEL-FUNCTIONS

Using results on multiply monotone functions, we establish the positiv ity of integrals of Bessel functions of the form integral-x/0 (x(mu) - t(mu))(lambda)t(alpha)J(beta)(t)dt, x > 0, where 0 < mu less-than-or- equal-to 1 less-than-or-equal-to lambda and alpha, beta satisfy variou s conditions. In particular, the result holds if - 1/2 less-than-or-eq ual-to alpha = beta less-than-or-equal-to 3/2 or if 3/2 = alpha less-t han-or-equal-to beta.