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and is closely related to [[Bessel function]]s of the second kind.
==Relation between Weber and Anger functions==
The Anger and Weber functions are related by
:<math>\sin(\pi \nu)\mathbf{J}_\nu(z) = \cos(\pi\nu)\mathbf{E}_\nu(z)-\mathbf{E}_{-\nu}(z)</math>
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so in particular if ν is not an integer they can be expressed as linear combinations of each other.
If ν is an integer then Anger functions '''J'''<sub>ν</sub> are the same as Bessel functions
J<sub>ν</sub>, and Weber functions can be expressed as finite linear combinations of [[Struve function]]s.
==Differential equations==
The Anger and Weber functions are solutions of inhomogenous forms of Bessel's equation <math>z^2y^{\prime\prime} + zy^\prime +(z^2-\nu^2)y = 0</math>. More precisely,
the Anger functions satisfy the equation
:<math>z^2y^{\prime\prime} + zy^\prime +(z^2-\nu^2)y = (z-\nu)\sin(\pi z)/\pi</math>
and the Weber functions satisfy the equation
:<math>z^2y^{\prime\prime} + zy^\prime +(z^2-\nu^2)y = -((z+\nu) + (z-\nu)\cos(\pi z))/\pi</math>
==References==
*{{AS ref|12|498}}
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