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    F(g(x))

    Series expansion at x = 0

    f(0) + x f'(0) + 1/2 x^2 (f''(0) + (-1 + 2 gamma + log(2 π)) f'(0)) + 1/24 x^3 ((-9 + 12 gamma ^2 - 2 π^2 + 3 log^2(2 π) + 12 gamma (log(2 π) - 2) - 6 log(2 π)) f'(0) + 4 (f^(3)(0) + 3 (-1 + 2 gamma + log(2 π)) f''(0))) + 1/144 x^4 (f'(0) (24 gamma ^3 - 6 gamma (3 + 2 π^2 - 3 log^2(2 π) + 12 log(2 π)) + π^2 (14 - 6 log(2 π)) + 36 gamma ^2 (log(2 π) - 3) + 3 (11 + log^3(2 π) - 3 log^2(2 π) - 9 log(2 π) - 8 polygamma(2, 1))) + 6 (f^(4)(0) + 6 f^(3)(0) (-1 + 2 gamma + log(2 π)) + 2 (-3 + 12 gamma ^2 - π^2 + 3 log^2(2 π) + 6 gamma (-3 + log(4) + 2 log(π)) - 6 log(2 π)) f''(0))) + O(x^5) (Taylor series)

    Series expansion at x = ∞

    f(exp(1/12 (-12 log(A) + 5 log(x) + 1 - 6 log(2 π)) - 1/(156 x^13) + 1/(144 x^12) + 691/(360360 x^11) - 691/(327600 x^10) - 1/(1188 x^9) + 1/(1056 x^8) + 1/(1680 x^7) - 1/(1440 x^6) - 1/(1260 x^5) + 1/(1008 x^4) + 1/(360 x^3) - 1/(240 x^2) + 1/4 x^2 (2 log(x) - 3) - 1/(12 x) + 1/2 x (-2 log(x) + 2 + log(2 π))))

    Derivative

    d/dx(f(G(x))) = 1/2 G(x) (-2 x + 2 (x - 1) polygamma(0, x) + 1 + log(2 π)) f'(G(x))

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