DLMF:10.22.E58 (Q3432): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.22.E58	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}\frac{J_{\nu}\left(at\right)J_{% \nu}\left(bt\right)}{t^{\lambda}}\mathrm{d}t=\frac{(ab)^{\nu}\Gamma\left(\nu-% \frac{1}{2}\lambda+\frac{1}{2}\right)}{2^{\lambda}(a^{2}+b^{2})^{\nu-\frac{1}{% 2}\lambda+\frac{1}{2}}\Gamma\left(\frac{1}{2}\lambda+\frac{1}{2}\right)}% \mathbf{F}\left(\frac{2\nu+1-\lambda}{4},\frac{2\nu+3-\lambda}{4};\nu+1;\frac{% 4a^{2}b^{2}}{(a^{2}+b^{2})^{2}}\right),}}

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DLMF:10.22.E58

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{\displaystyle{\displaystyle\Re(2\nu+1)>\Re\lambda>-1}}

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{\displaystyle{\displaystyle a\neq b}}

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{\displaystyle{\displaystyle\Re(2\nu+1)>\Re\lambda>-1}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aardec

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Defining formula

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

C5.S2.E1.m2asdec

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Defining formula

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

C1.S4.SS4.m1abedec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abedec

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