Difference between revisions of "Relationship between Bessel I sub -1/2 and cosh"

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Revision as of 00:28, 5 July 2015

Proposition: 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.

Proof: