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Jacobi Polynomials from Compatibility Conditions

Yang Chen·Mourad Ismail
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Abstract

We revisit the ladder operators for orthogonal polynomials and re-interpret two supplementary conditions as compatibility conditions of two linear over-determined systems; one involves the variation of the polynomials with respect to the variable z (spectral parameter) and the other a recurrence relation in n (the lattice variable). For the Jacobi weight w(x) = (1-x)^a(1+x)^b, x in [-1,1],we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.

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Yang Chen, Mourad Ismail. 2003-02-12. Jacobi Polynomials from Compatibility Conditions. https://arxiv.org/abs/math/0302142

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