Is there are analytic expression of the following definite integral?
$$ \int_{-1}^1 x^\alpha (1-x^2)^{\beta} P_l(x) P_m(x) \text{d}x $$
Is there are analytic expression of the following definite integral?
$$ \int_{-1}^1 x^\alpha (1-x^2)^{\beta} P_l(x) P_m(x) \text{d}x $$
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