# Anger function

From Encyclopedia of Mathematics

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.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Anger_function&oldid=16115

This article was adapted from an original article by A.P. Prudnikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article