Difference between revisions of "Differential equation for Jacobi P"
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Revision as of 03:35, 11 June 2016
Theorem
The Jacobi P polynomials $y(x)=P_n^{(\alpha,\beta)}(x)$ satisfy the differential equation $$(1-x^2)y(x)+[\beta-\alpha-(\alpha+\beta+2)x]y'(x)+n(n+\alpha+\beta+1)y(x)=0.$$
Proof
References
- 1975: Gabor Szegő: Orthogonal Polynomials ... (previous): Theorem 4.2.1
