DLMF:10.9.E15 (Q3083)

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Language	Label	Description	Also known as
English	DLMF:10.9.E15	No description defined

Statements

Defining formula

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

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DLMF:10.9.E15

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{\displaystyle{\displaystyle\Im(z\pm\zeta)>0}}

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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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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2andec

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Defining formula

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

C1.S4.SS4.m1andec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2ahdec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2afdec

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hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle\Im}}

C1.S9.E2.m2adec

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Defining formula

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

C1.S9.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3andec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1kdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1jdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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