math.com
Home    |    Teacher    |    Parents    |    Glossary    |    About Us
Homework Help Practice Ask An Expert Calculators & Tools Games Store
Email this page to a friend Email this page to a friend
Resources
· Cool Tools
· Formulas & Tables
· References
· Test Preparation
· Study Tips
· Wonders of Math
 
Search
Custom Search



Math Jobs


  
Gamma Function/b>
(Math | Calculus | Integrals | Special Functions | Gamma Function)
Gamma graph


Gamma(x) = (integral)(0 to inf) e -t t(x-1) dt

Gamma(x) = r x(integral)(0 to inf) e -rt t (x-1) dt

Gamma(x) = 2(integral)(0 to inf) e (-t^2) t (2x-1) dt

( Gamma(x)Gamma(y) ) / ( Gamma(x) + Gamma(y) ) = Beta(x,y)

Gamma(x+1) = x Gamma(x)

Gamma(x+1) = x!

Gamma(0+) = +inf

Gamma(1/2) = sqrt(PI)

Gamma(z) Gamma(1-z) = PI csc(PI z) Gamma'(1) = - gamma (Euler's constant = 0.577215...)

Gamma'(x) = Gamma(x) lim (n-->inf) [ ln(n) - sum (k=0..n-1) 1/(x+k) ]

Gamma Function Expansions
Gamma(x+1) = lim (k-->inf) kx 1*2*3*..*k
(x+1)(x+2)*..*(x+k)
Stirling's Asymptotic Series
Gamma(x+1) = sqrt(2PIx) xx e -x { 1 + 1/(12x) + 1/(288 x2) - 139/(51840 x3) - 571/(2488320 x4) + 163879/(209018880 x5) + 5246819/(75246796800 x6) - 534703531/(902961561600 x7) - ...}
(this is only an approximation, see note.)

Incomplete Gamma Functions:
Gamma(x, a) = (integral)(a to inf) e -t t (x-1) dt
gamma(x, a) = (integral)(0 to a) e -t t (x-1) dt

Gamma(x, a) + gamma(x, a) = Gamma(x)

  
 
  

 
Contact us | Advertising & Sponsorship | Partnership | Link to us

© 2000-2005 Math.com. All rights reserved.     Legal Notices.     Please read our Privacy Policy.