^3 square root x
| Input |
|---|
| x^(1/3) |
| Root |
| x = 0 |
| Derivative |
| d/dx(x^(1/3)) = 1/(3 x^(2/3)) |
| Indefinite integral |
| integral x^(1/3) dx = (3 x^(4/3))/4 + constant |
| Global minimum |
| min{x^(1/3)} = 0 at x = 0 |
| Series representation |
| x^(1/3) = sum_(n=0)^infinity binomial(1/3, n) (-1 + x)^n for abs(1 – x)<1 |
| 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 |