DLMF:10.22.E46 (Q3420)

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Language	Label	Description	Also known as
English	DLMF:10.22.E46	No description defined

Statements

Defining formula

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

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DLMF:10.22.E46

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{\displaystyle{\displaystyle\Re b>0}}

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{\displaystyle{\displaystyle-1<\Re\nu<2\Re\mu+\tfrac{3}{2}}}

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{\displaystyle{\displaystyle a>0}}

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{\displaystyle{\displaystyle\Re b>0}}

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{\displaystyle{\displaystyle-1<\Re\nu<2\Re\mu+\tfrac{3}{2}}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aaidec

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Defining formula

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

C5.S2.E1.m2aldec

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Defining formula

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

C1.S4.SS4.m1aasdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aasdec

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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.m2adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aaadec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1aedec

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