Difference between revisions of "Relationship between Anger function and Weber function"
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<strong>[[Relationship between Anger function and Weber function|Theorem]]:</strong> The following formula holds: | <strong>[[Relationship between Anger function and Weber function|Theorem]]:</strong> The following formula holds: | ||
$$\sin(\nu\pi)\mathbf{J}_{\nu}(z)=\cos(\nu \pi)\mathbf{E}_{\nu}(z)-\mathbf{E}_{-\nu}(z),$$ | $$\sin(\nu\pi)\mathbf{J}_{\nu}(z)=\cos(\nu \pi)\mathbf{E}_{\nu}(z)-\mathbf{E}_{-\nu}(z),$$ | ||
| − | where $\mathbf{J}_{\nu}$ denotes an [[Anger function]] and $\mathbf{E}_{\nu}$ denotes a Weber function. | + | where $\mathbf{J}_{\nu}$ denotes an [[Anger function]] and $\mathbf{E}_{\nu}$ denotes a [[Weber function]]. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 18:13, 28 June 2015
Theorem: The following formula holds: $$\sin(\nu\pi)\mathbf{J}_{\nu}(z)=\cos(\nu \pi)\mathbf{E}_{\nu}(z)-\mathbf{E}_{-\nu}(z),$$ where $\mathbf{J}_{\nu}$ denotes an Anger function and $\mathbf{E}_{\nu}$ denotes a Weber function.
Proof: █
