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Anger Function

A generalization of the Bessel Function of the First Kind defined by

{\mathcal J}_\nu(z) \equiv {1\over\pi} \int_0^\pi \cos(\nu\theta-z\sin\theta)\,d\theta.

If $\nu$ is an Integer $n$, then ${\mathcal J}_n(z) = J_n(z)$, where $J_n(z)$ is a Bessel Function of the First Kind. Anger's original function had an upper limit of $2\pi$, but the current Notation was standardized by Watson (1966).

See also Bessel Function, Modified Struve Function, Parabolic Cylinder Function, Struve Function, Weber Functions


Abramowitz, M. and Stegun, C. A. (Eds.). ``Anger and Weber Functions.'' §12.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 498-499, 1972.

Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.

© 1996-9 Eric W. Weisstein