Two infinite integrals of products of modified Bessel functions and powers of logarithms (Q1903672)

Starting from known integrals of Bessel functions new forms are derived that contain powers of logarithms. A typical example is \(\int_0^\infty t^{\rho-1} K_\nu (at) K_\lambda (at) \ln^m t dt\). When \(\nu\), \(\lambda\) are integers or half-integers the integrals can often be expressed in terms of finite sums. Several tables are given for these special cases.