Anger function
In mathematics, the Anger function, introduced by C. T. Anger (1855), is a function defined as J ν ( z ) = 1 π ∫ 0 π cos ( ν θ − z sin θ ) d θ {\displaystyle \mathbf {J} _{\nu }(z)={\frac {1}{\pi }}\int _{0}^{\pi }\cos(\nu \theta -z\sin \theta )\,d\theta } with complex parameter ν {\displaystyle \nu } and complex variable z {\displaystyle {\textit {z}}} . It is closely related to the Bessel functions.