Difference between revisions of "Relationship between Weber function and Anger function"
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| − | + | ==Theorem== | |
| − | + | 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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between Anger function and Weber function|next=Relation between Weber function and Struve function}}: 12.3.5 | ||
Latest revision as of 04:16, 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
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 12.3.5
