DLMF:9.6.E6 (Q2786)

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Language	Label	Description	Also known as
English	DLMF:9.6.E6	No description defined

Statements

Defining formula

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

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DLMF:9.6.E6

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Defining formula

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

C9.S2.SS1.m1abdec

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2adec

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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.m2addec

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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.m2addec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2addec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2addec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle z}}

C9.S1.XMD3.m1edec

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change of variable (locally)

Defining formula

{\displaystyle{\displaystyle\zeta}}

C9.S6.XMD1.m1edec

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Sitelinks

Wikipedia(0 entries)

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