Painleve solution of an integral equation
Y.Y. Atas, E. Bogomolny
TL;DR
This paper shows how a specific integral equation can be solved using the third kind Painleve equation, and expresses a special Painleve solution as a ratio of two infinite series of spheroidal functions.
Contribution
It introduces a novel method linking a particular integral equation to the Painleve III equation and expresses solutions in terms of spheroidal function series.
Findings
Integral equation solvable via Painleve III equation
Special Painleve solution expressed as ratio of spheroidal series
Provides explicit series representations for solutions
Abstract
It is demonstrated that a certain integral equation can be solved using the Painleve equation of third kind. Inversely, a special solution of this Painleve equation can be expressed as the ratio of two infinite series of spheroidal functions with known coefficients.
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Taxonomy
TopicsElectromagnetic Scattering and Analysis · Mathematical functions and polynomials · Iterative Methods for Nonlinear Equations