DLMF:10.7.E7 (Q3060)

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Language	Label	Description	Also known as
English	DLMF:10.7.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{H^{(1)}_{\nu}}\left(z\right)\sim-{H^{(2)}_{\nu}}% \left(z\right)\sim-(i/\pi)\Gamma\left(\nu\right)(\tfrac{1}{2}z)^{-\nu},}}

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DLMF:10.7.E7

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{\displaystyle{\displaystyle\Re\nu>0}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2addec

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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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asymptotic equality

Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.E1.m2aedec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

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Defining formula

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

C1.S9.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1abdec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1fdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1ddec

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