Gamma function

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/gamma-function

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the integral representation?Γ(z) = ∫₀^∞ t^(z-1)e^(-t) dt, valid for Re(z) > 0
2. What is the factorial generalization?Γ(n) = (n-1)! for positive integers n
3. What is the Gamma function and how is it different from a factorial?The Gamma function extends the idea of a factorial to all real and complex numbers. It is defined by an integral and gives values for numbers that are not whole numbers.
4. How do we find the Gamma function for a positive integer?For a positive integer n, the Gamma function equals (n-1)!. So if you plug in 5, you get 4!.

Analytic Continuation: Extending a function defined on a subset of the complex plane to a larger domain while preserving its analytic properties.
Special Function: A function that has specific mathematical properties and arises frequently in the solution of differential equations or in other areas of mathematics and science.
Complex Numbers: Numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit (√-1).