Formula:3526

Digital Library of Mathematical Functions ID 9.7.E19

${\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\frac{z^{1/4}e^{-\zeta}}{2\sqrt{\pi}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{v_{k}}{\zeta^{k}}+S_{n}(z)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\zeta}}$: change of variable (locally)
• ${\displaystyle{\displaystyle n}}$: index
• ${\displaystyle{\displaystyle S_{n}}}$: remainder function (locally)
• ${\displaystyle{\displaystyle v_{s}}}$: expansion coefficient
 

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