DLMF:10.22.E56 (Q3430)

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Language	Label	Description	Also known as
English	DLMF:10.22.E56	No description defined

Statements

Defining formula

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

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DLMF:10.22.E56

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

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{\displaystyle{\displaystyle 0<a<b}}

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{\displaystyle{\displaystyle\Re(\mu+\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.m2aapdec

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Defining formula

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

C5.S2.E1.m2aqdec

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Defining formula

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

C1.S4.SS4.m1abcdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abcdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aajdec

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$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

C15.S2.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1aodec

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Sitelinks

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