Resumen de A combinatorial identity and applications

Mariano Ferrari, Pablo A. Panzone

• An identity for the finite sum ∑N1 z^n/(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∞zn/(qn_(-r) ) , the Riemann zeta function and the Euler–Mascheroni constant. An irrationality result is also proved.