Monotonicity properties of determinants of special functions
Abbreviated Journal Title
polygamma functions; modified Bessel functions; confluent hypergeometric; function; Tricomi psi function; hermite polynomials; hypergeometric; function; Fibonacci numbers; complete monotonicity; absolute; monotonicity; GAMMA-FUNCTION; INEQUALITY; POLYNOMIALS; Mathematics
We prove the absolute monotonicity or complete monotonicity of some determinant functions whose entries involve psi((m))(x) = (d(m)/dx(m))[Gamma'(x)/Gamma(x)], modified Bessel functions I-v, K-v, the confluent hypergeometric function Phi, and the Tricomi function psi. 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.
"Monotonicity properties of determinants of special functions" (2007). Faculty Bibliography 2000s. 7251.