Formula:3510

Digital Library of Mathematical Functions ID 9.7.E5

${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)\sim\frac{e^{-\zeta}}{2\sqrt{\pi}z^{1/4}}\sum_{k=0}^{\infty}(-1)^{k}\frac{u_{k}}{\zeta^{k}},}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
• ${\displaystyle{\displaystyle\zeta}}$: change of variable (locally)
• ${\displaystyle{\displaystyle u_{s}}}$: expansion coefficient
 

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