A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants

Abstract

A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants is derived in this paper. In addition, we also report a formula for the Stieltjes constants in terms of the higher derivatives of the Riemann zeta function. A formula for the Stieltjes constants in terms of the (exponential) complete Bell polynomials containing the eta constants as the arguments is also derived.

References in corpus (6)

• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• A Set of Identities for a Class of Alternating Binomial Sums Arising in Computing Applications
• Theta and Riemann xi function representations from harmonic oscillator eigensolutions
• Some applications of the Stieltjes constants
• Polygamma theory, the Li/Keiper constants, and validity of the Riemann Hypothesis
• A Li-type criterion for zero-free half-planes of Riemann's zeta function

Cited by in corpus (5)

• The difference between two Stieltjes constants
• Some possible approaches to the Riemann Hypothesis via the Li/Keiper constants
• Some integrals involving the Stieltjes constants:Part II
• A generalisation of the Bernoulli numbers from the discrete to the continuous
• Some relations involving the higher derivatives of the Riemann zeta function