Formula:3649

Digital Library of Mathematical Functions ID 9.12.E23

${\displaystyle{\displaystyle\mathrm{Gi}\left(x\right)=\frac{4x^{2}}{3^{3/2}\pi^{2}}\pvint_{0}^{\infty}\frac{K_{1/3}\left(t\right)}{\zeta^{2}-t^{2}}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle x>0}}$

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
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}$: Cauchy principal value
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\zeta}}$: variable
 

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