An entire function which is a generalization of the Bessel function of the first kind
Anger's original function had an upper limit of , but the current notation was
standardized by Watson (1966).
The Anger function may also be written as
is a regularized hypergeometric
If is an integer , then , where is a Bessel
function of the first kind.
The Anger function is implemented in the Wolfram Language as AngerJ[nu,
See alsoAnger Differential Equation
, Bessel Function
, Parabolic Cylinder
, Struve Function
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ReferencesAbramowitz, 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 and Weber Function ." §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|AlphaAnger Function
Cite this as:
Weisstein, Eric W. "Anger Function." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AngerFunction.html