DLMF:10.32.E11 (Q3531)

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Language	Label	Description	Also known as
English	DLMF:10.32.E11	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle K_{\nu}\left(xz\right)=\frac{\Gamma\left(\nu+% \frac{1}{2}\right)(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{% \cos\left(xt\right)\mathrm{d}t}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}},}}

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DLMF:10.32.E11

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{\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}

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{\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}

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{\displaystyle{\displaystyle x>0}}

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}

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Defining formula

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

C5.S2.E1.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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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2agdec

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Defining formula

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

C1.S4.SS4.m1ajdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ajdec

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modified Bessel function of the second kind

Defining formula

{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S25.E3.m2afdec

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Defining formula

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

C1.S9.E7.m1addec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1acdec

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Defining formula

{\displaystyle{\displaystyle x}}

C10.S1.XMD4.m1bdec

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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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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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