My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Reply
 
LinkBack Thread Tools Display Modes
April 10th, 2015, 05:53 AM   #1
Newbie
 
Joined: Apr 2015
From: Finland

Posts: 1
Thanks: 0

Question (-0.5)!^2 = π? why?

Why does ((-0.5)!)^2 equal pi? To me it really doesnt make sense since of what i know of you cant even factorial negative numbers right??
Fredu4 is offline  
 
April 10th, 2015, 06:15 AM   #2
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

The "standard" definition of factorial is only for non-negative integers but it can be extended. It can, for example, be proven that the gamma function $\displaystyle \Gamma(n)= \int_0^\infty t^{n-1} e^{-t}dt= (n-1)!$ for n any positive integer. Even that integral is not defined for n a negative integer but it can be calculated for half integer, positive or negative, by an "integration by parts". Here "(-0.5)!)" is to be interpreted $\displaystyle \Gamma(0.5)= \int_0^\infty t^{1/2}e^{-t}dt$.
Country Boy is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
052, factorial, negative, pi number, question



Thread Tools
Display Modes






Copyright © 2019 My Math Forum. All rights reserved.