Difference between revisions of "Relationship between the Fransén–Robinson constant, e, pi, and logarithm"
From specialfunctionswiki
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2},$$ | + | $$F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2} \mathrm{d}x,$$ |
where $F$ denotes the [[Fransén–Robinson constant]], $e$ denotes [[E]], $\pi$ denotes [[pi]], and $\log$ denotes the [[logarithm]]. | where $F$ denotes the [[Fransén–Robinson constant]], $e$ denotes [[E]], $\pi$ denotes [[pi]], and $\log$ denotes the [[logarithm]]. | ||
Latest revision as of 03:06, 1 July 2017
Theorem
The following formula holds: $$F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2} \mathrm{d}x,$$ where $F$ denotes the Fransén–Robinson constant, $e$ denotes E, $\pi$ denotes pi, and $\log$ denotes the logarithm.
