A note on the Koekoeks’ differential equation for generalized Jacobi polynomials

✍ Scribed by H. Bavinck

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 65 KB
• Volume: 115
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00180-6

✦ Synopsis

In a recent paper (Di erential equations for generalized Jacobi polynomials, submitted for publication) Koekoek and Koekoek discovered a linear di erential equation for the polynomials {P ; ÿ; M; N n (x)} ∞ n=0 , which are orthogonal on [-1; 1] with respect to ( + ÿ + 2) 2 +ÿ+1 ( + 1) (ÿ + 1)

(1 -x) (1 + x) ÿ + M (x + 1) + N (x -1); ; ÿ¿-1; M; N¿0:

This di erential equation is of inÿnite order, except in a number of cases. It is the purpose of this note to reprove and interpret the results of the Koekoeks in the ÿnite-order cases in a short and easy way.