Difference between revisions of "Upper incomplete gamma"
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The upper incomplete gamma function $\Gamma$ is defined by | The upper incomplete gamma function $\Gamma$ is defined by | ||
$$\Gamma(s,x)=\displaystyle\int_x^{\infty} t^{s-1}e^{-t} dt.$$ | $$\Gamma(s,x)=\displaystyle\int_x^{\infty} t^{s-1}e^{-t} dt.$$ | ||
Revision as of 12:34, 17 September 2016
The upper incomplete gamma function $\Gamma$ is defined by $$\Gamma(s,x)=\displaystyle\int_x^{\infty} t^{s-1}e^{-t} dt.$$
Properties
Theorem
The following formula holds: $$E_n(z)=z^{n-1}\Gamma(1-n,z),$$ where $E_n$ denotes the exponential integral E and $\Gamma$ denotes the incomplete gamma function.
