Continuous Random Variable on Gamma Distribution

A random variable is said to have gamma distribution with parameters (t, λ), λ > 0, t > 0 if the function of concentration is given by

Gamma distribution is often found in practice as a distribution of the length of time a person has to wait until a number of events occur. More specifically, if the events occur randomly at intervals and fulfill the three axioms it turns out that the length of time people have to wait until a number of events occur is a gamma random variable with a parameter (n, λ). The gamma distribution with parameters (n, λ), n integers, is often called the Erlang -n distribution. (Note that if n = 1, this distribution is reduced to the exponent distribution).
Gamma distribution with λ = 1/2 and t = n / 2 (n posirif integers) is called the distribution of X2 (read chi-square). The distribution of chi-square in practice often appears as a distribution of errors that occur when trying to shoot a target in a dimensionless space n if every error in the coordinates spreads normally.
Integration by parts of Γ (t) yields,

For integer t values, say t = n, by applying the above gamma distribution equation we will get repeatedly,

Because   then for values ​​of n integers, 

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