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    Jacobi Polynomial

    Series expansion at x = 0

    P_n^(a, b)(0) + 1/2 x (a + b + n + 1) P_(n - 1)^(a + 1, b + 1)(0) + 1/8 x^2 (a + b + n + 1) (a + b + n + 2) P_(n - 2)^(a + 2, b + 2)(0) + 1/48 x^3 (a + b + n + 1) (a + b + n + 2) (a + b + n + 3) P_(n - 3)^(a + 3, b + 3)(0) + 1/384 x^4 (a + b + n + 1) (a + b + n + 2) (a + b + n + 3) (a + b + n + 4) P_(n - 4)^(a + 4, b + 4)(0) + O(x^5) (Taylor series)

    Derivative

    d/dx(P_n^(a, b)(x)) = 1/2 (a + b + n + 1) P_(n - 1)^(a + 1, b + 1)(x)

    Indefinite integral

    integral P_n^(a, b)(x) dx = (2 P_(n + 1)^(a - 1, b - 1)(x))/(a + b + n) + constant

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