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In this paper, we give an infinite sequence of inequalities involving the Riemann zeta function with even arguments ζ (2n) and the Chebyshev-Stirling numbers of the first kind. This result is based on a recent connection between the Riemann zeta function and the complete homogeneous symmetric functions [18]. An interesting asymptotic formula related to the n th complete homogeneous symmetric function is conjectured in this context:

An infinite sequence of inequalities involving special values of the Riemann zeta function