Difference between revisions of "Differential equation for Jacobi P"
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(Created page with "==Theorem== The Jacobi P polynomials $y(x)=P_n^{(\alpha,\beta)}(x)$ satisfy the differential equation $$(1-x^2)y''(x)+[\beta-\alpha-(\alpha+\beta+2)x]y'(x)+n(n+\alpha+\bet...") |
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==References== | ==References== | ||
| − | * {{BookReference|Orthogonal Polynomials|1975|Gabor Szegő|edpage = Fourth Edition|prev=Jacobi P of order 2n+1 with alpha=beta|findme}}: Theorem 4.2.1 | + | * {{BookReference|Orthogonal Polynomials|1975|Gabor Szegő|edpage = Fourth Edition|prev=Jacobi P of order 2n+1 with alpha=beta|next=findme}}: Theorem 4.2.1 |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 03:35, 11 June 2016
Theorem
The Jacobi P polynomials $y(x)=P_n^{(\alpha,\beta)}(x)$ satisfy the differential equation $$(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) ... (next): Theorem 4.2.1
