DLMF:9.5.E8

MaRDI QIDQ3478

• Label: DLMF:9.5.E8

Digital Library of Mathematical Functions ID 9.5.E8

${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{e^{-\zeta}\zeta^{\ifrac{-1}{6}}}{\sqrt{\pi}(48)^{\ifrac{1}{6}}\Gamma\left(\frac{5}{6}\right)}\int_{0}^{\infty}e^{-t}t^{-\ifrac{1}{6}}\left(2+\frac{t}{\zeta}\right)^{-\ifrac{1}{6}}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|<\frac{2}{3}\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma 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
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\zeta}}$: change of variable
 

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