On the zeros of the Pearcey integral and a Rayleigh-type equation
Classical Analysis and ODEs
2016-07-18 v1 Probability
Abstract
In this work we find a sequence of functions at which the Pearcey function is identically zero. The sequence of functions can be expressed in terms of a second order non-linear ODE, which happens to be the Rayleigh-type. As a byproduct of these facts, we develop a methodology to find a class of functions which solve the moving boundary problem of the heat equation. To this end, we make use of generalized Airy functions, which in some particular cases fall within the category of functions with infinitely many real zeros, studied by P\'olya.
Keywords
Cite
@article{arxiv.1506.02502,
title = {On the zeros of the Pearcey integral and a Rayleigh-type equation},
author = {Gerardo Hernández-del-Valle},
journal= {arXiv preprint arXiv:1506.02502},
year = {2016}
}