Difference between revisions of "Relationship between Bessel I sub 1/2 and sinh"
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<strong>[[Relationship between Bessel I sub 1/2 and sinh|Theorem]]:</strong> The following formula holds: | <strong>[[Relationship between Bessel I sub 1/2 and sinh|Theorem]]:</strong> The following formula holds: | ||
$$I_{\frac{1}{2}}(z)=\sqrt{\dfrac{2}{\pi z}}\sinh(z),$$ | $$I_{\frac{1}{2}}(z)=\sqrt{\dfrac{2}{\pi z}}\sinh(z),$$ | ||
| − | where $I_{\frac{1}{2}}$ denotes the [[ | + | where $I_{\frac{1}{2}}$ denotes the [[Modified Bessel I sub nu|modified Bessel function of the first kind]] and $\sinh$ denotes the [[Sinh|hyperbolic sine]]. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 00:31, 5 July 2015
Theorem: The following formula holds: $$I_{\frac{1}{2}}(z)=\sqrt{\dfrac{2}{\pi z}}\sinh(z),$$ where $I_{\frac{1}{2}}$ denotes the modified Bessel function of the first kind and $\sinh$ denotes the hyperbolic sine.
Proof: █
