Some computational formulas related the Riemann zeta-function tails

Abstract

Abstract In this paper we present two computational formulae for one kind of reciprocal sums related to the Riemann zeta-function at integer points s = 4 , 5 $s=4,5$ , which answers an open problem proposed by Lin (J. Inequal. Appl. 2016:32, 2016).

Keywords

• Riemann zeta-function
• inequality
• continued fraction
• telescoping method
• multiple-correction method