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 |