DLMF:10.22.E16

MaRDI QIDQ4087

• Label: DLMF:10.22.E16

Digital Library of Mathematical Functions ID 10.22.E16

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

Constraint(s)

${\displaystyle{\displaystyle n=0,1,2,\ldots}}$

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
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

Resources that cite this formula

No records found.