Anger Function

An entire function which is a generalization of the Bessel function of the first kind defined by


Anger's original function had an upper limit of 2pi, but the current notation was standardized by Watson (1966).

The Anger function may also be written as


where _1F^~_2(a;b,c;z) is a regularized hypergeometric function.

If nu is an integer n, then J_n(z)=J_n(z), where J_n(z) is a Bessel function of the first kind.

The Anger function is implemented in the Wolfram Language as AngerJ[nu, z].

See also

Anger Differential Equation, Bessel Function, Modified Struve Function, Parabolic Cylinder Function, Struve Function, Weber Functions

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Abramowitz, M. and Stegun, I. 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.Prudnikov, A. P.; Marichev, O. I.; and Brychkov, Yu. A. "The Anger Function J_nu(x) and Weber Function E_nu(x)." §1.5 in Integrals and Series, Vol. 3: More Special Functions. Newark, NJ: Gordon and Breach, p. 28, 1990.Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.

Referenced on Wolfram|Alpha

Anger Function

Cite this as:

Weisstein, Eric W. "Anger Function." From MathWorld--A Wolfram Web Resource.

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