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

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Title:	Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case
Authors:	Ho, C.-L.;Sasaki, R.;Takemura, K.
Contributors:	淡江大學物理學系
Date:	2013-03-04
Issue Date:	2013-04-11
Publisher:	Bristol: Institute of Physics Publishing Ltd.
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 P¨oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of the P¨oschlTeller 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 ∈ (−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.
Relation:	Journal of Physics A: Mathematical and Theoretical 46(11), 115205(27pages)
DOI:	10.1088/1751-8113/46/11/115205
Appears in Collections:	[Graduate Institute & Department of Physics] Journal Article

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