A combinatorial identity and applications

Mariano Ferrari ^[1] ; Pablo Panzone ^[2]
1. [1] Universidad Nacional de la Patagonia San Juan Bosco
  
  Universidad Nacional de la Patagonia San Juan Bosco
  
  Argentina
2. [2] Universidad Nacional del Sur
  
  Universidad Nacional del Sur
  
  Argentina
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 54, Nº. 1, 2013, págs. 35-42
Idioma: inglés
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Resumen
- 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.