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Carl Theodor Anger worked in astronomy and mathematics; the Anger function is associated with his name. This special function provides an example of how oscillatory integrals become reusable mathematical objects.

In modern notation it is defined by ${\mathbf{J}}_{\nu }(z)={\pi }^{-1}{\int }_0^{\pi }\cos (\nu \theta -z\sin \theta )d\theta$. Setting $z=0$ gives ${\mathbf{J}}_{\nu }(0)=\sin (\pi \nu )/(\pi \nu )$, with limiting value one at $\nu =0$. The example follows directly by integrating a cosine and illustrates how a general special-function representation yields elementary limiting cases.^[ref]

Institutional biographical record: www.deutsche-biographie.de/116311282.html