DLMF:10.27.E8 (Q3498): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.27.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle K_{\nu}\left(z\right)=\begin{cases}\tfrac{1}{2}% \pi ie^{\nu\pi i/2}{H^{(1)}_{\nu}}\left(ze^{\pi i/2}\right),&-\pi\leq% \operatorname{ph}z\leq\tfrac{1}{2}\pi,\\ -\tfrac{1}{2}\pi ie^{-\nu\pi i/2}{H^{(2)}_{\nu}}\left(ze^{-\pi i/2}\right),&-% \tfrac{1}{2}\pi\leq\operatorname{ph}z\leq\pi.\end{cases}}}

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DLMF:10.27.E8

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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.m2aadec

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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.m2aadec

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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.m2abdec

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Defining formula

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

C1.S9.E1.m2abdec

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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.m2addec

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