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

From specialfunctionswiki
Jump to: navigation, search
 
Line 1: Line 1:
<div class="toccolours mw-collapsible mw-collapsed">
+
==Theorem==
<strong>[[Relationship between Bessel I sub 1/2 and sinh|Theorem]]:</strong> The following formula holds:
+
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]].
<div class="mw-collapsible-content">
+
 
<strong>Proof:</strong> █
+
==Proof==
</div>
+
 
</div>
+
==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.

Proof

References