Difference between revisions of "Bessel J in terms of Bessel-Clifford"
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(Created page with "==Theorem== The following formula holds: $$J_n(z) = \left( \dfrac{z}{2} \right)^n \mathcal{C}_n\left( - \dfrac{z^2}{4} \right),$$ where $J_n$ denotes Bessel J and $\mathca...") |
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The following formula holds: | The following formula holds: | ||
$$J_n(z) = \left( \dfrac{z}{2} \right)^n \mathcal{C}_n\left( - \dfrac{z^2}{4} \right),$$ | $$J_n(z) = \left( \dfrac{z}{2} \right)^n \mathcal{C}_n\left( - \dfrac{z^2}{4} \right),$$ | ||
| − | where $J_n$ denotes [[Bessel J]] and $\mathcal{C}_n$ denotes [[Bessel-Clifford]]. | + | where $J_n$ denotes [[Bessel J]] and $\mathcal{C}_n$ denotes [[Bessel-Clifford function]]. |
==Proof== | ==Proof== | ||
Revision as of 01:05, 23 December 2016
Theorem
The following formula holds: $$J_n(z) = \left( \dfrac{z}{2} \right)^n \mathcal{C}_n\left( - \dfrac{z^2}{4} \right),$$ where $J_n$ denotes Bessel J and $\mathcal{C}_n$ denotes Bessel-Clifford function.
