DLMF:9.6.E3 (Q2783)

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DLMF:9.6.E3
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Statements

${\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\pi^{-1}(z/\sqrt{3})K_% {\pm 2/3}\left(\zeta\right)=(z/3)\left(I_{2/3}\left(\zeta\right)-I_{-2/3}\left% (\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})e^{-\pi i/6}{H^{(1)}_{2/3}}\left(% \zeta e^{\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{-5\pi i/6}{H^{(1)}_{-2/3}}% \left(\zeta e^{\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{\pi i/6}{H^{(2)}_{2/% 3}}\left(\zeta e^{-\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{5\pi i/6}{H^{(2)% }_{-2/3}}\left(\zeta e^{-\pi i/2}\right),}}$
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DLMF:9.6.E3
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${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$
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${\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$
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${\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$
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${\displaystyle{\displaystyle\pi}}$
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${\displaystyle{\displaystyle\mathrm{e}}}$
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${\displaystyle{\displaystyle\mathrm{i}}}$
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${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$
${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$
${\displaystyle{\displaystyle z}}$
${\displaystyle{\displaystyle\zeta}}$