Formula:3220

Digital Library of Mathematical Functions ID 8.6.E8

${\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{-\mathrm{i}z^{a}}{2\sin\left(\pi a\right)}\int_{-1}^{(0+)}t^{a-1}e^{zt}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle a\notin\mathbb{Z}}}$
${\displaystyle{\displaystyle z\neq 0}}$
${\displaystyle{\displaystyle a\notin\mathbb{Z}}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}$: incomplete gamma function
• ${\displaystyle{\displaystyle\mathbb{Z}}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\notin}}$:
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: parameter
 

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