Difference between revisions of "Relationship between Bessel I sub 1/2 and sinh"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | 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 [[Modified Bessel I sub nu|modified Bessel function of the first kind]] and $\sinh$ denotes the [[Sinh|hyperbolic sine]]. | 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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:54, 8 June 2016
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.
