A COMBINATORIAL IDENTITY AND APPLICATIONS

作者：Ferrari Mariano^*; Panzone Pablo A

来源：Union Matematica Argentina. Revista, 2013, 54(1): 35-42.

• Combinatorial identity
• irrationalities
• Riemann zeta function
• Euler-Mascheroni constant

An identity for the finite sum Sigma(N)(1) z(n)/q(n-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 Sigma(infinity)(1) z(n)/q(n-r), the Riemann zeta function and the Euler-Mascheroni constant. An irrationality result is also proved.

• 出版日期2013