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arXiv · 1210.0207

Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case

C. -L. Ho·R. Sasaki·K. Takemura
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Abstract

The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the Pöschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of the Pöschl-Teller potential, we obtain several families of explicit and global solutions of certain second order Fuchsian differential equations with an apparent singularity of characteristic exponent -2 and -1. They form orthogonal polynomials over $x\in(-1,1)$ with weight functions of the form $(1-x)^α(1+x)^β/\{(ax+b)^4q(x)^2\}$, in which $q(x)$ is a polynomial in $x$.

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C. -L. Ho, R. Sasaki, K. Takemura. 2013-03-06. Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case. https://doi.org/10.1088/1751-8113%2F46%2F11%2F115205

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