Another Euler Constant: The Value of an Euler Integral

Allouche, Jean-Paul

doi:10.2478/udt-2024-0002

Abstract

We show many occurrences in various contexts of the constant $E_{u} : = \frac{π^{2}}{4} log 2 - \frac{7}{8} ζ (3) = 2.507907542$ {E_u}: = {{{\pi ^2}} \over 4}\log 2 - {7 \over 8}\zeta \left( 3 \right) = 2.507907542 ... Since this constant is related to an integral studied by Euler, we propose to name it after Euler.

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Another Euler Constant: The Value of an Euler Integral

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