DLMF:10.22.E47 (Q3421)

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Language	Label	Description	Also known as
English	DLMF:10.22.E47	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}\frac{t^{\nu}Y_{\nu}\left(at% \right)}{t^{2}+b^{2}}\mathrm{d}t=-b^{\nu-1}K_{\nu}\left(ab\right),}}

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DLMF:10.22.E47

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{\displaystyle{\displaystyle a>0,\Re b>0,-\tfrac{1}{2}<\Re\nu<\tfrac{5}{2}}}

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Bessel function of the second kind

Defining formula

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

C10.S2.E3.m2afdec

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Defining formula

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

C1.S4.SS4.m1aatdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aatdec

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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.m2aadec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aabdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1afdec

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