Difference between revisions of "Fransén–Robinson constant"

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[[Category:SpecialFunction]]

Revision as of 18:59, 24 May 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.

Proposition (Relation to $e$ and $\pi$): $F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2}.$

Proof: proof goes here █

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