DLMF:9.10.E18

MaRDI QIDQ3599

• Label: DLMF:9.10.E18

Digital Library of Mathematical Functions ID 9.10.E18

${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{3z^{5/4}e^{-(2/3)z^{3/2}}}{4\pi}\*\int_{0}^{\infty}\frac{t^{-3/4}e^{-(2/3)t^{3/2}}\mathrm{Ai}\left(t\right)}{z^{3/2}+t^{3/2}}\mathrm{d}t,}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: 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
 

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