gamma

Gamma special function

📝 Syntax

• R = gamma(M)

📥 Input argument

• M - a real single or real double matrix.

📤 Output argument

• R - result of gamma function.

📄 Description

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)

• $\Gamma(1/2) = \sqrt{\pi}$

💡 Example

R = gamma([-pi:0.1:pi])

🔗 See also

gammaln, factorial.

🕔 History

Version	📄 Description
1.0.0	initial version