Title

Monotonicity properties of determinants of special functions

Authors

Authors

M. E. H. Ismail;A. Laforgia

Comments

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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

DOI Link

http://dx.doi.org/10.1007/s00365-005-0627-4

Language

English

First Page

1

Last Page

9

WOS Identifier

WOS:000246084100001

ISSN

0176-4276

Recommended Citation

"Monotonicity properties of determinants of special functions" (2007). Faculty Bibliography 2000s. 7251.
https://stars.library.ucf.edu/facultybib2000/7251