论文信息 - On a differential equation for Koornwinder's generalized Laguerre polynomials

On a differential equation for Koornwinder's generalized Laguerre polynomials

Koornwinder's generalized Laguerre polynomials {L` N(X)}oo0 are orthogonal on the interval [0, oo) with respect to the weight function 1 f-)xae x + N3(x), (x > -1, N > 0. We show that these polynomials ['(a+ for N > 0 satisfy a unique differential equation of the form 00 N ai (x)y(1)(x) + xy " (x) + ( + 1-x)y'(x) + ny(x) = 0, 1=0 where {a,(x)}1o are continuous functions on the real line and {a'(x)}1i are independent of the degree n . If N > 0, only in the case of nonnegative integer values of a this differential equation is of finite order.

R. Koekoek | J. Koekoek

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