Math Fun Facts!
hosted by the Harvey Mudd College Math Department created, authored and ©1999-2010 by Francis Su
Subscribe to our RSS feed   or follow us on Twitter.
Get a random Fun Fact!
No subject limitations
Search only in selected subjects
    Calculus or Analysis
    Number Theory
    Other subjects
  Select Difficulty  
Enter keywords 

  The Math Fun Facts App!
  List All : List Recent : List Popular
  About Math Fun Facts / How to Use
  Contributors / Fun Facts Home
© 1999-2010 by Francis Edward Su
All rights reserved.

From the Fun Fact files, here is a Fun Fact at the Medium level:

Gamma Function

The Gamma function is an amazing integral:

Gamma(x) = INTEGRALt=0 to infinity tx-1 e-t dt .

Using integration by parts, you can show that this function satisfies the property

Gamma(x) = (x-1) Gamma(x-1).

Using Gamma(1)=1, you can calculate Gamma(2), Gamma(3),...
Does this remind you of anything?

Surprise: the Gamma function satisfies Gamma(n) = Factorial(n-1).
(I would have used the notation "!" but you might think I was just excited!)

So you can think of the Gamma function as being a continuous form of the factorial function. It satisfies lots of cool properties; here is just one:

Gamma(1/2) = Sqrt[Pi].

Presentation Suggestions:
Calculus students might be challenged to compute Gamma(2), Gamma(3), etc. and discover the connection with the factorial function. You may wish to assign the integration by parts as a homework exercise prior to presenting this Fun Fact.

The Math Behind the Fact:
The Gamma function is an important function in analysis, complex analysis, combinatorics, and probability.

How to Cite this Page:
Su, Francis E., et al. "Gamma Function." Math Fun Facts. <>.

Keywords:    calculus, continuous factorial
Subjects:    calculus, analysis
Level:    Medium
Fun Fact suggested by:   Michael Moody
Suggestions? Use this form.
Click to rate this Fun Fact...
    *   Awesome! I totally dig it!
    *   Fun enough to tell a friend!
    *   Mildly interesting
    *   Not really noteworthy
and see the most popular Facts!
New: get the MathFeed iPhone App!

Brings you news and views on math:
showcasing its power, beauty, and humanity

Want another Math Fun Fact?

For more fun, tour the Mathematics Department at Harvey Mudd College!