Home / Get Math Help
F(g(x))
Series expansion at x = ∞
f(exp(1/4 x (-3 x + 2 (x - 2) log(x) + 4 + 2 log(π) + log(4))) ((e^(1/12) x^(5/12))/(A sqrt(2 π)) - (e^(1/12) (1/x)^(7/12))/(12 (A sqrt(2 π))) - (e^(1/12) (1/x)^(19/12))/(1440 (A sqrt(2 π))) + (157 e^(1/12) (1/x)^(31/12))/(51840 A sqrt(2 π)) + (65911 e^(1/12) (1/x)^(43/12))/(87091200 A sqrt(2 π)) - (918227 e^(1/12) (1/x)^(55/12))/(1045094400 (A sqrt(2 π))) + O((1/x)^(61/12))))
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))