Difference between revisions of "Relationship between Anger function and Weber function"
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| − | + | ==Theorem== | |
| − | + | 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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
Revision as of 04:10, 6 June 2016
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.
