Formula:3647

Digital Library of Mathematical Functions ID 9.12.E21

${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=-\frac{1}{\pi}\int_{0}^{\infty}\exp\left(-\tfrac{1}{3}t^{3}-\tfrac{1}{2}zt\right)\cos\left(\tfrac{1}{2}\sqrt{3}zt+\tfrac{2}{3}\pi\right)\mathrm{d}t.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}$: Scorer function (inhomogeneous Airy function)
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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