DLMF:9.6.E2 (Q2782)

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Language	Label	Description	Also known as
English	DLMF:9.6.E2	No description defined

Statements

Defining formula

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

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DLMF:9.6.E2

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Defining formula

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

C9.S2.SS1.m1adec

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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.m2adec

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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.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

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Defining formula

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

C1.S9.E1.m2adec

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modified Bessel function of the first kind

Defining formula

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

C10.S25.E2.m2adec

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modified Bessel function of the second kind

Defining formula

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

C10.S25.E3.m2adec

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Sitelinks

Wikipedia(0 entries)

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