Gamma Functions
• Γ(z)—Returns the value of the Euler gamma function of z.
The following relationships involving the gamma function may be useful:
◦ Γ(z + 1) = z · Γ(z)
◦ Γ(z)·Γ(1 − z) = π · csc(π · z)
◦ Γ(n + 1) = n!
• Γ(a, x)—Returns the value of the incomplete gamma function of x with parameter a. Γ(a, 0) = Γ(a).
• lnΓ(z)—Returns the natural log of the Euler gamma function, evaluated at z.
To type Γ, press G,Ctrl+G.
Use the lnΓ function to return smaller results, then scale them.
• Psi(y)—Returns the derivative of the natural log of the Γ(y) function.
Arguments
• z is a dimensionless, real or complex scalar, undefined for z = 0, −1, −2...
For Γ(z), only arguments −107 ≤ Re(z) ≤ 171 and −106 ≤ Im(z) ≤ 106 can be evaluated without numerical overflow. For complex z, Γ(z) is the analytic continuation of the real function.
• a is a dimensionless, positive, real scalar.
• x is a dimensionless, positive, real scalar, or 0.
• y is a real number.