DLMF:9.6.E22

MaRDI QIDQ3500

• Label: DLMF:9.6.E22

Digital Library of Mathematical Functions ID 9.6.E22

${\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\tfrac{1}{2}\pi^{-1/2}z^{1/4}W_{0,2/3}\left(2\zeta\right)=-3^{1/6}\pi^{-1/2}\zeta^{4/3}e^{-\zeta}U\left(\tfrac{7}{6},\tfrac{7}{3},2\zeta\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: Kummer confluent hypergeometric function
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\zeta}}$: change of variable (locally)
 

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