A fractional integral of order 1/2. The semi-integral of t^λ is given by D^(-1/2) t^λ = (t^(λ + 1/2) Γ(λ + 1))/(Γ(λ + 3/2)), so the semi-integral of the constant function f(t) = c is given by D^(-1/2) c = clim_(λ->0) (t^(λ + 1/2) Γ(λ + 1))/(Γ(λ + 3/2)) = 2csqrt(t/π).

fractional integral | integral