Gamma function imaginary argument

1. Can you use the gamma function for complex numbers?
2. How do you find the gamma function of a complex number?
3. What is the value of gamma Γ ½ is?
4. What is the value of Γ 2?

Can you use the gamma function for complex numbers?

The gamma function is extended to all complex numbers, with a real part >0, except for at zero and negative integers. Figure 1 gives the curve for gamma function (Eqn. 2). At negative integers, the gamma function has simple poles, making it a meromorphic function (Figure 1).

How do you find the gamma function of a complex number?

The Gamma function is defined by Γ(z)=∫∞0tz−1e−tdt when ℜz>0.

What is the value of gamma Γ ½ is?

The key is that Γ(1/2)=√π.

What is the value of Γ 2?

Similarly, using a technique from calculus known as integration by parts, it can be proved that the gamma function has the following recursive property: if x > 0, then Γ(x + 1) = xΓ(x). From this it follows that Γ(2) = 1 Γ(1) = 1; Γ(3) = 2 Γ(2) = 2 × 1 = 2!; Γ(4) = 3 Γ(3) = 3 × 2 × 1 = 3!; and so on.