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:<math>z^2y^{\prime\prime} + zy^\prime +(z^2-\nu^2)y = -\frac{z+\nu+(z-\nu)\cos(\pi \nu)}{\pi}.</math>
==Recurrence Relations==
The Anger function satisfy this inhomogeneous form of [[recurrence relation]]<ref name=DLMF/>
:<math>z\mathbf{J}_{\nu-1}(z)+z\mathbf{J}_{\nu+1}(z)=2\nu\mathbf{J}_\nu(z)-\frac{2\sin\pi\nu}{\pi}</math>
While the Weber function satisfy this inhomogeneous form of [[recurrence relation]]<ref name=DLMF/>
:<math>z\mathbf{E}_{\nu-1}(z)+z\mathbf{E}_{\nu+1}(z)=2\nu\mathbf{E}_\nu(z)-\frac{2(1-\cos\pi\nu)}{\pi}</math>
==References==
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