 Home    |    Teacher    |    Parents    |    Glossary    |    About Us              Email this page to a friend   Resources  · Cool Tools · Formulas & Tables · References · Test Preparation · Study Tips · Wonders of Math Search  Gamma Function/b> (Math | Calculus | Integrals | Special Functions | Gamma Function)   (x) =  e -t t(x-1) dt (x) = r x  e -rt t (x-1) dt (x) = 2  e (-t^2) t (2x-1) dt ( (x) (y) ) / ( (x) + (y) ) = Beta(x,y) (x+1) = x (x) (x+1) = x! (0+) = +  (1/2) = (PI) (z) (1-z) = PI csc(PI z) '(1) = - gamma (Euler's constant = 0.577215...) '(x) = (x) lim (n--> ) [ ln(n) - (k=0..n-1) 1/(x+k) ] Function Expansions (x+1) = lim (k--> ) kx 1*2*3*..*k (x+1)(x+2)*..*(x+k)
Stirling's Asymptotic Series (x+1) = (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: (x, a) =  e -t t (x-1) dt (x, a) =  e -t t (x-1) dt (x, a) + (x, a) = (x) 