Difference between revisions of "Relationship between Bessel I sub -1/2 and cosh"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$I_{-\frac{1}{2}}(z)=\sqrt{\dfrac{2}{\pi z}} \cosh(z),$$ | $$I_{-\frac{1}{2}}(z)=\sqrt{\dfrac{2}{\pi z}} \cosh(z),$$ | ||
where $I_{-\frac{1}{2}}$ denotes [[Modified Bessel I sub nu|the modified Bessel function of the first kind]] and $\cosh$ denotes the [[Cosh|hyperbolic cosine]]. | where $I_{-\frac{1}{2}}$ denotes [[Modified Bessel I sub nu|the modified Bessel function of the first kind]] and $\cosh$ denotes the [[Cosh|hyperbolic cosine]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:01, 17 June 2016
Theorem
The following formula holds: $$I_{-\frac{1}{2}}(z)=\sqrt{\dfrac{2}{\pi z}} \cosh(z),$$ where $I_{-\frac{1}{2}}$ denotes the modified Bessel function of the first kind and $\cosh$ denotes the hyperbolic cosine.
