Anger Function
المؤلف:
Abramowitz, M. and Stegun, I. A
المصدر:
"Anger and Weber Functions." §12.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
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18-11-2018
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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 
, 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].
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.
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