Jacobi Polynomials from Compatibility Conditions
نویسندگان
چکیده
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)(1 + x) , x ∈ [−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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تاریخ انتشار 2004