DLMF:10.9.E10 (Q3077): Difference between revisions

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Latest revision as of 15:13, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:10.9.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{H^{(1)}_{\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.E10

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

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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.m2adec

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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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Defining formula

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

C1.S4.SS4.m1aidec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2abdec

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Defining formula

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

C1.S9.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aidec

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Defining formula

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

C1.S9.E7.m1acdec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1gdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1edec

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