Difference between revisions of "Bessel J in terms of Bessel-Clifford"
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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 the [[Bessel-Clifford]] function. |
==Proof== | ==Proof== | ||
Latest revision as of 10:44, 11 January 2017
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 the Bessel-Clifford function.
