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),$$ |
| + | where $I_{\frac{1}{2}}$ denotes the [[Modfied Bessel I sub nu|modified Bessel function of the first kind]] and $\sinh$ denotes the [[Sinh|hyperbolic sine]]. | ||
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
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Revision as of 00:30, 5 July 2015
Theorem: The following formula holds: $$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: █
