|
|
|
|
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*}
|
"integral representations of the Mascheroni constant" is owned by rspuzio.
|
|
(view preamble | get metadata)
Cross-references: integrals, Mascheroni's constant
There is 1 reference to this entry.
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.
Accessed 1467 times total.
Classification:
| AMS MSC: | 40A25 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Approximation to limiting values ) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|