# Differential equation for Jacobi P

From specialfunctionswiki

## 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