Math2.org Math Tables: Special Functions |
(Math) |
(x) = t^{x-1} e^{-t} dt (Gamma function)
B(x,y) = t^{x-1} (1-t)^{y-1}dt (Beta function)
Ei(x) = e^{-t}/t dt (exponential integral) or it's variant, NONEQUIVALENT form:
Ei(x) = + ln(x) + (e^{^t} - 1)/t dt = gamma + ln(x) + (n=1..inf)x^{^n}/(n*n!)li(x) = 1/ln(t) dt (logarithmic integral)
Si(x) = sin(t)/t dt = PI/2 - sin(t)/t dt
Ci(x) = - cos(t)/t dt = gamma + ln(x) + (cos(t) - 1) / t dt (cosine integral)
(error function)
dilog(x) = ln(t) (1-t)^{-1} dt
Psi(n,x) = n^{th} derivative of Psi(x)
W(x) = inverse of x e^{x}
(laguerre polynomial degree n. (n) meaning n^{th} derivative)
Dirichlet's beta function