Difference between revisions of "Anger three-term recurrence"
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| − | <strong>[[Anger recurrence | + | <strong>[[Anger three-term recurrence|Theorem]]:</strong> The following formula holds: |
$$\textbf{J}_{\nu-1}(z)+\textbf{J}_{\nu+1}(z)=\dfrac{2\nu}{z}\textbf{J}_{\nu}(z)-\dfrac{2}{\pi z}\sin(\pi \nu),$$ | $$\textbf{J}_{\nu-1}(z)+\textbf{J}_{\nu+1}(z)=\dfrac{2\nu}{z}\textbf{J}_{\nu}(z)-\dfrac{2}{\pi z}\sin(\pi \nu),$$ | ||
where $\textbf{J}_{\nu}$ denote the [[Anger function]], $\pi$ denotes [[pi]], and $\sin$ denotes [[sine]]. | where $\textbf{J}_{\nu}$ denote the [[Anger function]], $\pi$ denotes [[pi]], and $\sin$ denotes [[sine]]. | ||
Revision as of 16:45, 23 May 2016
Theorem: The following formula holds: $$\textbf{J}_{\nu-1}(z)+\textbf{J}_{\nu+1}(z)=\dfrac{2\nu}{z}\textbf{J}_{\nu}(z)-\dfrac{2}{\pi z}\sin(\pi \nu),$$ where $\textbf{J}_{\nu}$ denote the Anger function, $\pi$ denotes pi, and $\sin$ denotes sine.
Proof: █
