DLMF:10.22.E24

MaRDI QIDQ4095

• Label: DLMF:10.22.E24

Digital Library of Mathematical Functions ID 10.22.E24

${\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{\mu}\left(z{\sin^{2}}\theta\right)J_{\nu}\left(z{\cos^{2}}\theta\right)\cot\theta\mathrm{d}\theta=\tfrac{1}{2}\mu^{-1}J_{\mu+\nu}\left(z\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\mu>0,\Re\nu>-1}}$

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
• ${\displaystyle{\displaystyle\cot\NVar{z}}}$: cotangent 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
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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