# Differential equation for Jacobi P

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The Jacobi P polynomials $y(x)=P_n^{(\alpha,\beta)}(x)$ satisfy the differential equation $$(1-x^2)y' '(x)+[\beta-\alpha-(\alpha+\beta+2)x]y'(x)+n(n+\alpha+\beta+1)y(x)=0.$$