Series with zeta values and infinite products

Abstract

In this short note, we point out an interesting connection between series with zeta values and certain infinite products. Using this connection we give a closed-form evaluation of a special class of series with zeta values in the coefficients.

Keywords:

• Riemann's zeta function
• infinite products
• Gamma function

2010 Mathematics Subject Classification:

• Primary: 11M06
• Secondary: 33B15