Weber function

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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].


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