Consider the Jacobi polynomials denoted by $ P_n^{(\alpha,\beta)}(x) $ corresponding to the weight function $w(x) = (1+x)^{\alpha } (1-x)^ {\beta} $ defined on $(-1,1)$. Why is that the condition $ \alpha > \beta > -1 $ and $ \alpha + \beta + 1 $ be a non-negative integer is imposed ?
2026-03-26 17:31:33.1774546293
Orthogonality of Jacobi polynomials and the parameters
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This condition is used to ensure that the Jacobi polynomials are orthogonal.