Difference between revisions of "Fransén–Robinson constant"

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$$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx,$$
 
$$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx,$$
 
where $\dfrac{1}{\Gamma}$ denotes the [[reciprocal gamma function]].
 
where $\dfrac{1}{\Gamma}$ denotes the [[reciprocal gamma function]].
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<strong>Proposition (Relation to [[e|$e$]] and [[pi|$\pi$]]):</strong> $F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2}.$
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=Properties=
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[[Relationship between the Fransén–Robinson constant, e, pi, and logarithm]]
<strong>Proof:</strong> proof goes here █
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[[Category:SpecialFunction]]
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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