| Input |
|---|
| x^(-3/2) |
| Result |
| 1/x^(3/2) |
| Roots |
| (no roots exist) |
| Derivative |
| d/dx(x^(-3/2)) = -3/(2 x^(5/2)) |
| Indefinite integral |
| integral 1/x^(3/2) dx = -2/sqrt(x) + constant |
| Limit |
| lim_(x-> ± infinity) 1/x^(3/2) = 0 |
| Series representation |
| 1/x^(3/2) = sum_(n=0)^infinity binomial(-3/2, 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 |