Formula:3641

Digital Library of Mathematical Functions ID 9.12.E15

${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=\frac{3^{-2/3}}{\pi}\*\sum_{k=0}^{\infty}\cos\left(\frac{2k-1}{3}\pi\right)\Gamma\left(\frac{k+1}{3}\right)\frac{(3^{1/3}z)^{k}}{k!},}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}$: 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
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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