DLMF:9.6.E7 (Q2787): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:9.6.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{Ai}'\left(-z\right)=(z/3)\left(J_{2/3}% \left(\zeta\right)-J_{-2/3}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})% \left(e^{-\pi i/6}{H^{(1)}_{2/3}}\left(\zeta\right)+e^{\pi i/6}{H^{(2)}_{2/3}}% \left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{-5\pi i/6}{H^{(1)}_% {-2/3}}\left(\zeta\right)+e^{5\pi i/6}{H^{(2)}_{-2/3}}\left(\zeta\right)\right% ),}}

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DLMF:9.6.E7

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Defining formula

{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}

C9.S2.SS1.m1acdec

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Bessel function of the first kind

Defining formula

{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2aadec

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Bessel function of the third kind (or Hankel function)

Defining formula

{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}

C10.S2.E5.m2aedec

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Bessel function of the third kind (or Hankel function)

Defining formula

{\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}

C10.S2.E6.m2aedec

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