Gamma function



The gamma function came as a result of Eulers efforts to generalize the factorial function to non-integer values.

The factorial function is given by

$$n! = n(n-1)(n-2) ... 3 \times 2 \times 1$$         for all integers, $$n > 0$$

$$n! = 1$$        , $$n = 0$$

= History =

A complete historical perspective of the Gamma function is given in the work of Godefroy

Louis Franois Antoine Arbogast (1759 - 1803) introduced factorial

The ﬁrst reported use of the gamma symbol for this function was by Legendre in 1839, and (the integral form of) the Gamma function is often referred to as Eulers 2nd integral

Polynomial Approximation of Γ(z + 1)
= Gamma function Approximations =

Polynomial Approximation of Γ(z + 1) within 0 ≤ z ≤ 1 Hastings

= Series expansions =

= Applications =

time based occurrences

Gamma distribution

incomplete Gamma
I

= Digamma =

normalized form of the logarithmic derivative, also known is the psi function