A physicist’s guide to explicit summation formulas involving zeros of Bessel functions and related spectral sums

DOI10.1142/S0129055X21300028zbMath1476.35102arXiv1904.11190OpenAlexW3109556707MaRDI QIDQ5156078

Denis S. Grebenkov

Publication date: 14 October 2021

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.11190

zbMATH Keywords

diffusionsummation formulasheat kernelBessel functionsLaplacian eigenvaluesspectral sums

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (3)

The Bessel zeta function ⋮ On Fourier–Bessel series and the Kneser–Sommerfeld expansion ⋮ Extreme hitting probabilities for diffusion*

Cites Work

• On an identity for zeros of Bessel functions
• Critical times in multilayer diffusion. I: Exact solutions
• Diffusion and reaction among traps: Some theoretical and simulation results
• Transient temperature distribution in a multilayer medium subject to radiative surface cooling
• Semi-analytical computation of Laplacian Green functions in three-dimensional domains with disconnected spherical boundaries
• Diffusion across semi-permeable barriers: spectral properties, efficient computation, and applications
• Mass diffusion through two-layer porous media: an application to the drug-eluting stent
• A Guide to First-Passage Processes
• Geometrical Structure of Laplacian Eigenfunctions
• First exit times of harmonically trapped particles: a didactic review
• Some Continuous Monte Carlo Methods for the Dirichlet Problem
• On some infinite series involving the zeros of Bessel functions of the first kind
• Reciprocal Power Sums of Differences of Zeros of Special Functions
• Diffusions and Elliptic Operators
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