Difference between revisions of "Upper incomplete gamma"
From specialfunctionswiki
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| − | The incomplete gamma function $\Gamma$ is defined by | + | The upper incomplete gamma function $\Gamma$ is defined by |
$$\Gamma(s,x)=\displaystyle\int_x^{\infty} t^{s-1}e^{-t} dt.$$ | $$\Gamma(s,x)=\displaystyle\int_x^{\infty} t^{s-1}e^{-t} dt.$$ | ||
=Properties= | =Properties= | ||
{{:Relationship between the exponential integral and incomplete gamma function}} | {{:Relationship between the exponential integral and incomplete gamma function}} | ||
Revision as of 03:41, 23 April 2015
The upper incomplete gamma function $\Gamma$ is defined by $$\Gamma(s,x)=\displaystyle\int_x^{\infty} t^{s-1}e^{-t} dt.$$
Contents
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.
