DLMF:10.22.E75

MaRDI QIDQ4147

• Label: DLMF:10.22.E75

Digital Library of Mathematical Functions ID 10.22.E75

${\displaystyle{\displaystyle\int_{0}^{\infty}Y_{\nu}\left(at\right)J_{\nu}\left(bt\right)J_{\nu}\left(ct\right)t^{1+\nu}\mathrm{d}t=\begin{cases}-\dfrac{(abc)^{\nu}(-A)^{-\nu-\frac{1}{2}}}{\pi^{\frac{1}{2}}2^{\nu+1}\Gamma\left(\frac{1}{2}-\nu\right)},&0<a<|b-c|,\\ 0,&|b-c|<a<b+c,\\ \dfrac{(abc)^{\nu}(-A)^{-\nu-\frac{1}{2}}}{\pi^{\frac{1}{2}}2^{\nu+1}\Gamma\left(\frac{1}{2}-\nu\right)},&a>b+c.\end{cases}}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the second kind
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle A}}$: area
 

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