  The Euler-Mascheroni constant is calculated by three novel representations
over these sets respectively: 1) Tur\'an moments, 2) coefficients of Jensen
polynomials for the Taylor series of the Riemann Xi function at s=1/2+i.t and
3) even coefficients of the Riemann Xi function around s=1/2. These findings
support the acceptance of the property of hyperbolicity of Jensen polynomials
within the scope of the Riemann Hypothesis due to exactness on the
approximations calculated not only for the Euler-Mascheroni constant but also
for the Bernoulli numbers and the even derivatives of the Riemann Xi function
at s=1/2. The new formulas are linked to similar patterns observed in the
formulation of the Akiyama-Tanigawa algorithm based on the Gregory coefficients
of second order and lead to understanding the Riemann zeta function as a bridge
between the Gregory coefficients and other relevant sets
