Monotonicity properties of determinants of special functions

    Authors

    M. E. H. Ismail;A. Laforgia

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Constr. Approx.

    Keywords

    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

    Abstract

    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.

    Journal Title

    Constructive Approximation

    Volume

    26

    Issue/Number

    1

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    1

    Last Page

    9

    WOS Identifier

    WOS:000246084100001

    ISSN

    0176-4276

    Share

    COinS