Function gamma 

pub fn gamma(z: &Expression) -> Expression

Gamma function Γ(z)

The Gamma function extends the factorial to complex numbers: Γ(n) = (n-1)! for positive integers n

Mathematical Properties

• Γ(n+1) = n·Γ(n) (functional equation)
• Γ(1) = 1
• Γ(1/2) = √π
• Pole at non-positive integers

Numerical Evaluation

Float inputs are evaluated numerically using Lanczos approximation (14-digit precision). Half-integers return exact symbolic forms (e.g., Γ(1/2) = √π).

Input Validation

• NaN or infinity inputs return NaN
• Non-positive integers are poles (return symbolic or error)

Arguments

• z - Expression to evaluate gamma function at

Examples

use mathhook_core::{Expression, Number};
use mathhook_core::functions::special::gamma;

let result = gamma(&Expression::Number(Number::Integer(5)));
assert_eq!(result, Expression::Number(Number::Integer(24)));

let half = gamma(&Expression::Number(Number::Float(0.5)));