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)
