Painlev\'e II transcendents and their squares
P.L. Robinson
TL;DR
This paper explores the connection between Painlevé II transcendents and a specific equation from Ince's master list, shedding light on their mathematical relationship.
Contribution
It establishes a novel link between Painlevé II solutions and Ince's equation, expanding understanding of special functions.
Findings
Identifies a new relationship between Painlevé II and Ince's equation
Provides analytical expressions connecting the two equations
Enhances the theory of special functions and integrable systems
Abstract
We examine the relationship between the homogeneous second Painlev\'e equation and equation from the master list recorded by Ince.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions