DLMF:10.32.E19 (Q3539): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.32.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle K_{\mu}\left(z\right)K_{\nu}\left(z\right)=\frac{% 1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\Gamma\left(t+\frac{1}{2}\mu+\frac% {1}{2}\nu\right)\Gamma\left(t+\frac{1}{2}\mu-\frac{1}{2}\nu\right)\Gamma\left(% t-\frac{1}{2}\mu+\frac{1}{2}\nu\right)\Gamma\left(t-\frac{1}{2}\mu-\frac{1}{2}% \nu\right)}{\Gamma\left(2t\right)}(\tfrac{1}{2}z)^{-2t}\mathrm{d}t,}}

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DLMF:10.32.E19

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{\displaystyle{\displaystyle c>\tfrac{1}{2}(|\Re\mu|+|\Re\nu|),|\operatorname{% ph}z|<\tfrac{1}{2}\pi}}

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Defining formula

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

C5.S2.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.m2apdec

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Defining formula

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

C1.S4.SS4.m1ardec

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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.m3ardec

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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.m2aldec

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Defining formula

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

C1.S9.E7.m1ajdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1agdec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1odec

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Sitelinks

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