One of the most important mathematical constants is Euler-Mascheroni constant that is the limit of the sequence --------------------------------  and is denoted by gamma. Some other developed constants known as Euler type constants are introduced in order to generalize the above constant. In the present paper, inspired by the functional sequence derivative of the limit summand of functions (i...

As a natural generalization of the Euler–Mascheroni constant $\gamma $, Y. Ihara introduced Euler–Kronecker _K$ attached to any number field $K$. He obtained bounds on conditional upon generalized Riemann hypothesis. I

In this study, we derive a new representation for the Euler-Mascheroni constant and present various expressions classical related to Riemann zeta function. Also, proved that \(\gamma\) is not algebraic if Schanuel conjecture true.

An identity for the finite sum ∑N 1 z qn−r is given. Related sums (or series) were studied by Scherk, Clausen, Ramanujan, Shanks, Andrews, and others. We use such identity to give new formulas for ∑∞ 1 z qn−r , the Riemann zeta function and the Euler–Mascheroni constant. An irrationality result is also proved.