Formula:4818

Digital Library of Mathematical Functions ID 12.5.E7

${\displaystyle{\displaystyle V\left(a,z\right)=\frac{e^{-\frac{1}{4}z^{2}}}{2\pi}\*\left(\int_{-ic-\infty}^{-ic+\infty}+\int_{ic-\infty}^{ic+\infty}\right)e^{zt-\frac{1}{2}t^{2}}t^{a-\frac{1}{2}}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle-\pi<\operatorname{ph}{t}<\pi}}$
${\displaystyle{\displaystyle-\pi<\operatorname{ph}{t}<\pi}}$
${\displaystyle{\displaystyle c>0}}$

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
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle V\left(\NVar{a},\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
 

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