Difference between revisions of "Relationship between Weber function and Anger function"

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==Theorem==
<strong>[[Relationship between Weber function and Anger function|Theorem]]:</strong> The following formula holds:
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The following formula holds:
 
$$\sin(\nu \pi)\mathbf{E}_{\nu}(z)=\mathbf{J}_{-\nu}(z)-\cos(\nu \pi)\mathbf{J}_{\nu}(z),$$
 
$$\sin(\nu \pi)\mathbf{E}_{\nu}(z)=\mathbf{J}_{-\nu}(z)-\cos(\nu \pi)\mathbf{J}_{\nu}(z),$$
 
where $\mathbf{E}_{\nu}$ denotes a [[Weber function]] and $\mathbf{J}_{\nu}$ denotes an [[Anger function]].
 
where $\mathbf{E}_{\nu}$ denotes a [[Weber function]] and $\mathbf{J}_{\nu}$ denotes an [[Anger function]].
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<strong>Proof:</strong>  █
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==Proof==
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==References==

Revision as of 04:09, 6 June 2016

Theorem

The following formula holds: $$\sin(\nu \pi)\mathbf{E}_{\nu}(z)=\mathbf{J}_{-\nu}(z)-\cos(\nu \pi)\mathbf{J}_{\nu}(z),$$ where $\mathbf{E}_{\nu}$ denotes a Weber function and $\mathbf{J}_{\nu}$ denotes an Anger function.

Proof

References