Jacobi polynomials from compatibility conditions
Abbreviated Journal Title
Proc. Amer. Math. Soc.
ORTHOGONAL POLYNOMIALS; FREUD POLYNOMIALS; Mathematics, Applied; Mathematics
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)(alpha) (1+x)beta, x is an element of [-1, 1], we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.
Proceedings of the American Mathematical Society
"Jacobi polynomials from compatibility conditions" (2005). Faculty Bibliography 2000s. 5062.