DLMF:10.22.E57 (Q3431)

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Language	Label	Description	Also known as
English	DLMF:10.22.E57	No description defined

Statements

Defining formula

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

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DLMF:10.22.E57

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{\displaystyle{\displaystyle\Re(\mu+\nu+1)>\Re\lambda>0}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aaqdec

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Defining formula

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

C5.S2.E1.m2ardec

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Defining formula

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

C1.S4.SS4.m1abddec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abddec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aakdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1apdec

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