Formula:3650

Digital Library of Mathematical Functions ID 9.12.E24

${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=\frac{3^{-2/3}}{2\pi^{2}i}\int_{-i\infty}^{i\infty}\Gamma\left(\tfrac{1}{3}+\tfrac{1}{3}t\right)\Gamma\left(-t\right)(3^{1/3}e^{\pi i}z)^{t}\mathrm{d}t,}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}$: Scorer function (inhomogeneous Airy function)
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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