Difference between revisions of "Fransén–Robinson constant"
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The Fransén–Robinson constant is defined to be the number $F$ given by the formula | The Fransén–Robinson constant is defined to be the number $F$ given by the formula | ||
| − | $$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx | + | $$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx,$$ |
| + | where $\dfrac{1}{\Gamma}$ denotes the [[reciprocal gamma function]]. | ||
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | ||
<strong>Proposition (Relation to [[e|$e$]] and [[pi|$\pi$]]):</strong> $F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2}.$ | <strong>Proposition (Relation to [[e|$e$]] and [[pi|$\pi$]]):</strong> $F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2}.$ | ||
Revision as of 18:33, 7 February 2016
The Fransén–Robinson constant is defined to be the number $F$ given by the formula $$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx,$$ where $\dfrac{1}{\Gamma}$ denotes the reciprocal gamma function.
