Anger function

Summary

The Anger function $\mathbf{J}_\nu$ is the function obtained by using Bessel's integral formula for an arbitrary order $\nu$. For integer $\nu$ it equals the Bessel function of the first kind $J_\nu$; for other $\nu$ it does not. Its companion is the Weber function $\mathbf{E}_\nu$, defined with a sine in place of the cosine. Both solve inhomogeneous forms of Bessel's equation.