gamma computes the gamma function.

The gamma function is defined by the integral:

$$\Gamma(z) = \int_0^{\infty} t^{z-1} e^{-t} \, dt$$

for

$$\text{Re}(z) > 0$$

The gamma function extends the factorial function to real and complex numbers:

$$\Gamma(n) = (n-1)!$$

for positive integers

$$n$$

Key properties include:

• $$\Gamma(z+1) = z\Gamma(z)$$ (recurrence relation)
• $$\Gamma(1/2) = \sqrt{\pi}$$

gammalnfactorial