Is the Euler–Mascheroni constant an algebraic number or a transcendental number?

Posted byDavePosted inMathematical Analysis, Number Theory, Numbers, Open ProblemsTags:, , ,
Is the Euler–Mascheroni constant (\gamma ) an algebraic number or a transcendental number?

Valid Assumption (Convergence): 1. \gamma = \frac{\sqrt{z^{2} - 1}}{2}.

Remark: We tentatively assume z is an algebraic number (rational number) where 1.52 < z < 1.53 .

We can apply Newton’s Method to equation one and study its convergence with regards to \gamma .

Warning: This may be a difficult problem…

Dave.

Relevant Reference Links:

Mascheroni_constant;

Newton’s_Method;

Is the Euler–Mascheroni constant an algebraic number?

Published by Dave

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