Anger function

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The function


which satisfies the inhomogeneous Bessel equation:

For integers is the Bessel function of order (cf. Bessel functions). For non-integer the following expansion is valid:

The asymptotic expansion

is valid for and .

The functions have been named after C.T. Anger [1], who studied functions of the type (*), but with as the upper limit of the integral.


[1] C.T. Anger, Neueste Schr. d. Naturf. d. Ges. i. Danzig , 5 (1855) pp. 1–29
[2] G.N. Watson, "A treatise on the theory of Bessel functions" , 1–2 , Cambridge Univ. Press (1952)
How to Cite This Entry:
Anger function. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.P. Prudnikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article