Monotonicity Properties of Determinants of Special Functions |
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Authors: | Mourad E.H. Ismail Andrea Laforgia |
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Affiliation: | (1) Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA;(2) Department of Mathematics, Roma Tre University, Largo San Leonardo Murialdo 1, 00146 Rome, Italy |
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Abstract: | We prove the absolute monotonicity or complete monotonicity of some determinant functions whose entries involve 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. |
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Keywords: | Polygamma functions Confluent hypergeometric function Tricomi Ψ function Hermite polynomials Hypergeometric function Fibonacci numbers Spherical functions Complete monotonicity Absolute monotonicity |
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