Formula:2665

Digital Library of Mathematical Functions ID 5.9.E3

${\displaystyle{\displaystyle c^{-z}\Gamma\left(z\right)=\int_{-\infty}^{\infty}|t|^{2z-1}e^{-ct^{2}}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle\Re z>0}}$
${\displaystyle{\displaystyle c>0}}$
${\displaystyle{\displaystyle\Re z>0}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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