Title

Monotonicity Properties Of Determinants Of Special Functions

Keywords

Absolute monotonicity; Complete monotonicity; Confluent hypergeometric function; Fibonacci numbers; Hermite polynomials; Hypergeometric function; Modified Bessel functions; Polygamma functions; Spherical functions; Tricomi Ψ function

Abstract

We prove the absolute monotonicity or complete monotonicity of some determinant functions whose entries involve ψ(m)(x) = (d m/dxm)[Γ′(x)/Γ(x)], modified Bessel functions Iν, Kν, the confluent hypergeometric function Φ, and the Tricomi function Ψ. 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. © 2006 Springer.

Publication Date

6-1-2007

Publication Title

Constructive Approximation

Volume

26

Issue

1

Number of Pages

1-9

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00365-005-0627-4

Socpus ID

34147121583 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/34147121583

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