Gamma function

• How to Calculate the Factorial of a Noninteger
  The factorial of a noninteger is calculated with the Gamma function, giving values such as 1/2! = √π/2 and 3.5! = 105√π/16.
• How to Expand the Lower Incomplete Gamma Function for s < 0
  For negative noninteger s, the lower incomplete gamma function has a convergent series in powers of x; its defining integral from zero diverges.
• How to Compute ∫₀¹ xᵐ(1 − xⁿ)ᵖ dx
  For n > 0, m > −1, and p > −1, substitute t = xⁿ to evaluate the integral as a Beta function and, if desired, Gamma functions.
• Mean and Variance of the Weibull Distribution
  For a Weibull distribution with shape k and scale λ, the mean is λΓ(1+1/k) and the variance is λ²[Γ(1+2/k)−Γ(1+1/k)²].