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