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[parent] integral representations of the Mascheroni constant (Theorem)

Mascheroni's constant can be expressed by the following integrals: \begin{eqnarray*} \gamma &=& - \int_0^1 \log (- \log x) \, dx \\ \gamma &=& - \int_0^\infty e^{-x} \log x \, dx \\ \gamma &=& \int_0^\infty \left( {1 \over e^t - 1} - {1 \over t e^t} \right) \, dt \\ \gamma &=& \int_0^\infty \left( {1 \over t} - {1 \over 1 + t} - {1 \over t e^t} \right) \, dt \\ \end{eqnarray*}




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Cross-references: integrals, Mascheroni's constant
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This is version 5 of integral representations of the Mascheroni constant, born on 2006-05-02, modified 2006-05-02.
Object id is 7891, canonical name is IntegralRepresesntationOfTheMascheroniConstant.
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Classification:
AMS MSC40A25 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Approximation to limiting values )

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