DLMF:9.6.E8 (Q2788): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:9.6.E8	No description defined

Statements

Defining formula

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

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DLMF:9.6.E8

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Defining formula

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

C9.S2.SS1.m2abdec

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2abdec

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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.m2afdec

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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.m2afdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2afdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2afdec

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Defining formula

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

C1.S9.E1.m2afdec

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Defining formula

{\displaystyle{\displaystyle z}}

C9.S1.XMD3.m1gdec

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Sitelinks

Wikipedia(0 entries)

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