Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity

TL;DR

This paper constructs explicit solutions for specific second-order differential equations with a high-degree apparent singularity using multi-indexed Laguerre polynomials, advancing understanding of such equations.

Contribution

It introduces a method to generate explicit solutions for equations with apparent singularities of characteristic exponent -2, utilizing multi-indexed Laguerre polynomials.

Findings

Explicit solutions for equations with apparent singularity of exponent -2

Use of multi-indexed Laguerre polynomials to adjust parameters

Enhanced understanding of differential equations with high-degree singularities

Abstract

Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent -2 are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.