Monotonicity properties of determinantes of special functions

We prove the absolute monotonicity or complete monotonicity of some determinant functions whose entries involve ψ(m)(x) = (dm/dxm)[ (x)/(x)], modified Bessel functions Iν , Kν , the confluent hypergeometric function, and the Tricomi function . Our results recover and generalize some known determinantal inequalities. We also show that a certain determinant formed by the Fibonacci numbers are nonnegative while determinants involving Hermite polynomials of imaginary arguments are shown to be completely monotonic functions.