DLMF:10.22.E14

MaRDI QIDQ4085

• Label: DLMF:10.22.E14

Digital Library of Mathematical Functions ID 10.22.E14

${\displaystyle{\displaystyle\int_{0}^{\pi}J_{2\nu}\left(2z\sin\theta\right)\cos\left(2\mu\theta\right)\mathrm{d}\theta=\pi\cos\left(\mu\pi\right)J_{\nu+\mu}\left(z\right)J_{\nu-\mu}\left(z\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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