Difference between revisions of "Relationship between Bessel I sub -1/2 and cosh"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Proposition:</strong> The following formula holds: $$I_{-\frac{...") |
|||
(2 intermediate revisions by the same user not shown) | |||
Line 1: | Line 1: | ||
− | + | ==Theorem== | |
− | + | The following formula holds: | |
$$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.