E^sqrtx

E^sqrtx

Input
e^(sqrt(x))
Roots
(no roots exist)
Series expansion at x=0
1 + sqrt(x) + x/2 + x^(3/2)/6 + x^2/24 + x^(5/2)/120 + x^3/720 + x^(7/2)/5040 + x^4/40320 + x^(9/2)/362880 + O(x^5)
(Puiseux series)
Derivative
d/dx(e^(sqrt(x))) = e^(sqrt(x))/(2 sqrt(x))
Indefinite integral
integral e^(sqrt(x)) dx = 2 e^(sqrt(x)) (sqrt(x) – 1) + constant
Global minimum
min{e^(sqrt(x))} = 1 at x = 0
Integral representation
(1 + z)^a = ( integral_(-i infinity + gamma)^(i infinity + gamma) (Gamma(s) Gamma(-a – s))/z^s ds)/((2 pi i) Gamma(-a)) for (0

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