DLMF:10.17.E13 (Q3182)

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Language	Label	Description	Also known as
English	DLMF:10.17.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\rselection{{H^{(1)}_{\nu}}\left(z\right)\\ {H^{(2)}_{\nu}}\left(z\right)}=\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{% \pm i\omega}\left(\sum_{k=0}^{\ell-1}(\pm i)^{k}\frac{a_{k}(\nu)}{z^{k}}+R_{% \ell}^{\pm}(\nu,z)\right),}}

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DLMF:10.17.E13

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{\displaystyle{\displaystyle\ell=1,2,\ldots}}

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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.m2abdec

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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.m2abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aidec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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Defining formula

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

C1.S9.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1jdec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1jdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1kdec

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expansion (locally)

Defining formula

{\displaystyle{\displaystyle a_{k}(\nu)}}

C10.S17.XMD1.m1edec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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