Formula:3598

Digital Library of Mathematical Functions ID 9.10.E17

${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\alpha-1}\mathrm{Ai}\left(t\right)\mathrm{d}t=\frac{\Gamma\left(\alpha\right)}{3^{(\alpha+2)/3}\Gamma\left(\tfrac{1}{3}\alpha+\tfrac{2}{3}\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\alpha>0}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
 

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