# Did anyone ever try to determine or propose the algebraic role of Euler-Mascheroni constant?

Both the constant $$\pi$$ and the constant $$e$$ have clear algebraic roles in complex numbers and in differential calculus.

But did anyone ever propose an algebraic role for Euler-Mascheroni constant $$\gamma$$?

• What is "algebraic role"? Just some analytic identities involving it? – Conifold Apr 8 at 21:00
• @Conifold well, algebraic role is serving as unity, invariant or fixed point under certain basic operations or being a result of basic operations applied to unity or zero. For instance, $e^x$ is invariant under differentiation, and $e^{1/e}$ is fixed point of tetration. – Anixx Apr 8 at 21:17
• Well, $-\gamma=\psi(1)$ like $e=\exp(1)$, but the digamma $\psi$ is more analogous to $\ln$ than to $\exp$. It has the same relation to the difference operator, $\psi(x+1)-\psi(x)=\frac1x$, that $\ln x$ has to the derivative, $(\ln x)'=\frac1x$. So what would be the algebraic role for something like $\ln 2$? – Conifold Apr 10 at 8:41