DLMF:9.6.E5 (Q2785): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:9.6.E5	No description defined

Statements

Defining formula

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

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DLMF:9.6.E5

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Defining formula

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

C9.S2.SS1.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.m2acdec

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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.m2acdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2acdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2acdec

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Defining formula

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

C1.S9.E1.m2acdec

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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.m2acdec

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Defining formula

{\displaystyle{\displaystyle z}}

C9.S1.XMD3.m1ddec

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Sitelinks

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