Difference between revisions of "Fransén–Robinson constant"

From specialfunctionswiki
Jump to: navigation, search
 
Line 2: Line 2:
 
$$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx,$$
 
$$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx,$$
 
where $\dfrac{1}{\Gamma}$ denotes the [[reciprocal gamma function]].
 
where $\dfrac{1}{\Gamma}$ denotes the [[reciprocal gamma function]].
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
+
 
<strong>Proposition (Relation to [[e|$e$]] and [[pi|$\pi$]]):</strong> $F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2}.$
+
=Properties=
<div class="mw-collapsible-content">
+
[[Relationship between the Fransén–Robinson constant, e, pi, and logarithm]]
<strong>Proof:</strong> proof goes here █
 
</div>
 
</div>
 
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 20:17, 20 June 2016

The Fransén–Robinson constant is defined to be the number $F$ given by the formula $$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx,$$ where $\dfrac{1}{\Gamma}$ denotes the reciprocal gamma function.

Properties

Relationship between the Fransén–Robinson constant, e, pi, and logarithm