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. A.P. Prudnikov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Weber_function&oldid=13892
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098
