DLMF:10.22.E38

MaRDI QIDQ4109

• Label: DLMF:10.22.E38

Digital Library of Mathematical Functions ID 10.22.E38

${\displaystyle{\displaystyle\int_{0}^{1}tJ_{\nu}\left(\alpha_{\ell}t\right)J_{\nu}\left(\alpha_{m}t\right)\mathrm{d}t=\left(\frac{a^{2}}{b^{2}}+\alpha_{\ell}^{2}-\nu^{2}\right)\frac{(J_{\nu}\left(\alpha_{\ell}\right))^{2}}{2\alpha_{\ell}^{2}}\delta_{\ell,m},}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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