Differential equations for symmetric generalized ultraspherical polynomials

Author:
Roelof Koekoek

Journal:
Trans. Amer. Math. Soc. **345** (1994), 47-72

MSC:
Primary 33C45; Secondary 34B24, 34L10

MathSciNet review:
1260202

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Abstract | References | Similar Articles | Additional Information

Abstract: We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval with respect to the weight function

In the special case that and we find all differential equations of the form

*n*.

We show that if only for nonnegative integer values of there exists exactly one differential equation which is of finite order .

By using quadratic transformations we also obtain differential equations for the polynomials for all and .

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DOI:
https://doi.org/10.1090/S0002-9947-1994-1260202-3

Article copyright:
© Copyright 1994
American Mathematical Society