Inequalities and monotonicity properties for zeros of Hermite functions

DOI10.1017/S0308210500027463zbMath0944.33006MaRDI QIDQ4243030

Martin E. Muldoon, Árpád Elbert

Publication date: 18 September 2000

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hermite functionsconfluent hypergeometric functionsprincipal solutions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items

Fractional Sturm–Liouville problems for Weber fractional derivatives, Árpád Elbert, 1939--2001: A memorial tribute., A new firing paradigm for integrate and fire stochastic neuronal models, Continuous ranking of zeros of special functions, Unnamed Item, Hitting time in Erlang loss systems with moving boundaries, Criterion for the Sobolev well-posedness of the Dirichlet problem for the Poisson equation in Lipschitz domains. I, Some Laplace transforms and integral representations for parabolic cylinder functions and error functions, Improving Beckner's bound via Hermite functions, A Nicholson-Type Integral for the Product of Two Parabolic Cylinder Functions D ν ( x ) D ν (− x ) AT ℜν≪0, Some recent results on the zeros of Bessel functions and orthogonal polynomials, Product of parabolic cylinder functions involving Laplace transforms of confluent hypergeometric functions, Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications, Rome, Italy, June 18--22, 2001. Dedicated to the memory of Professor Árpád Elbert, On the transition of Charlier polynomials to the Hermite function, Properties of zeros of orthogonal polynomials and related functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions
• On the Hellmann-Feynman theorem and the variation of zeros of certain special functions
• Metric spaces and completely monontone functions
• On the Square of the Zeros of Bessel Functions
• On the Convexity of the Zeros of Bessel Functions
• 17.—An Upper Bound for the Largest Zero of Hermite's Function with Applications to Subharmonic Functions
• Monotonicity and Convexity Properties of Zeros of Bessel Functions
• Product Formulas and Nicholson-Type Integrals for Jacobi Functions. I: Summary of Results
• On the Derivative with Respect to a Parameter of a Zero of a Sturm–Liouville Function
• A Supplement to the Sturm Separation Theorem, with Applications
• Higher Monotonicity Properties of Certain Sturm-Liouville Functions. III
• Ordinary Differential Equations