DLMF:10.9.E11 (Q3078)

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No description defined

Language	Label	Description	Also known as
English	DLMF:10.9.E11	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{H^{(2)}_{\nu}}\left(z\right)=-\frac{e^{\frac{1}{2% }\nu\pi i}}{\pi i}\int_{-\infty}^{\infty}e^{-iz\cosh t-\nu t}\mathrm{d}t,}}

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DLMF:10.9.E11

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{\displaystyle{\displaystyle-\pi<\operatorname{ph}z<0}}

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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.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ajdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1ajdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aedec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2acdec

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Defining formula

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

C1.S9.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ajdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1addec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1hdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1fdec

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