# Weber function

From Encyclopedia of Mathematics

The function

where is a complex number and is a real number. It satisfies the inhomogeneous Bessel equation

For non-integral the following expansion is valid:

If and , the following asymptotic expansion is valid:

where is the Neumann function. If is not an integer, the Weber function is related to the Anger function by the following equations:

The Weber functions were first studied by H. Weber [1].

#### References

[1] | H.F. Weber, Zurich Vierteljahresschrift , 24 (1879) pp. 33–76 |

[2] | G.N. Watson, "A treatise on the theory of Bessel functions" , 1 , Cambridge Univ. Press (1952) |

**How to Cite This Entry:**

Weber function.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Weber_function&oldid=13892

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