Jacobi Polynomials from Compatibility Conditions

Details Jacobi Polynomials from Compatibility Conditions Jacobi Polynomials from Compatibility Conditions

2003-02-12

arxiv.org/abs/math/0302142v1

Mathematics

Classical Analysis and ODEs

11 pages 0 figures

Scientific paper

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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