DLMF:10.43.E10 (Q3624): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.43.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{x}^{\infty}e^{t}t^{-\nu}K_{\nu}\left(t\right% )\mathrm{d}t=\frac{e^{x}x^{-\nu+1}}{2\nu-1}(K_{\nu}\left(x\right)+K_{\nu-1}% \left(x\right)),}}

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DLMF:10.43.E10

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

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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.m2aedec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aidec

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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.m2abdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1abdec

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Defining formula

{\displaystyle{\displaystyle x}}

C10.S1.XMD4.m1fdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1fdec

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Sitelinks

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