Formula:3687

Digital Library of Mathematical Functions ID 9.13.E25

${\displaystyle{\displaystyle A_{k}\left(z,p\right)=\frac{1}{2\pi i}\int_{\mathscr{L}_{k}}t^{-p}\exp\left(zt-\tfrac{1}{3}t^{3}\right)\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle p\in\mathbb{C}}}$
${\displaystyle{\displaystyle k=1,2,3}}$
${\displaystyle{\displaystyle p\in\mathbb{C}}}$

Symbols List

• ${\displaystyle{\displaystyle A_{\NVar{k}}\left(\NVar{z},\NVar{p}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathbb{C}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\mathscr{L}}}$: integration path
 

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