 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/7/b/i/solution

Substituting

z = 1

into the defining Gamma integral gives

Γ (1) = \int_{0}^{\infty} e^{- t} d t = [- e^{- t}]_{0}^{\infty} = 1.

Both endpoints are convergent, so no continuation of the Gamma function is needed here.

 New to topics? Read the docs here!