DLMF:9.6.E4 (Q2784): Difference between revisions

Revision as of 14:26, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:9.6.E4	No description defined

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

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DLMF:9.6.E4

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

C9.S2.SS1.m2adec

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

C10.S2.E5.m2abdec

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@@ Property / Symbols used @@
+Bessel function of the third kind (or Hankel function)
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$ 
\HankelH{1}{\NVar{\nu}}@{\NVar{z}}
+xml-id: C10.S2.E5.m2abdec