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 
, but the current notation was
standardized by Watson (1966).
The Anger function may also be written as
where 
is a regularized hypergeometric
function.
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,
z].
See also
Anger Differential Equation,
Bessel Function,
Modified
Struve Function,
Parabolic Cylinder
Function,
Struve Function,
Weber
Functions
Explore with Wolfram|Alpha
References
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 
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|Alpha
Anger Function
Cite this as:
Weisstein, Eric W. "Anger Function." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AngerFunction.html
Subject classifications
