# Math Help - MGF of gamma distribution

1. ## MGF of gamma distribution

Hi all
I am new here

I just dont understand how to get the moment generating function of gamma distribution wit pdf:
f(x;α,λ) = [λ^αx^(α−1)e^−λx]/Γ(α) , x ≥ 0; α,λ > 0.

can anybody help me plz asap

thanks alot

2. Originally Posted by ma19sa
Hi all
I am new here

I just dont understand how to get the moment generating function of gamma distribution wit pdf:
f(x;α,λ) = [λ^αx^(α−1)e^−λx]/Γ(α) , x ≥ 0; α,λ > 0.

can anybody help me plz asap

thanks alot
Where are you stuck? The problem boils down to calculating $\int_0^{+ \infty} e^{-x( \lambda - t)} x^{a - 1} \, dx$ which in turn boils down to calculating $\int_0^{+ \infty} e^{-y} y^{a - 1} \, dy$ and this is a well known integral ....