DLMF:10.9.E1

MaRDI QIDQ3764

• Label: DLMF:10.9.E1

Digital Library of Mathematical Functions ID 10.9.E1

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

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
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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