Some relations involving the higher derivatives of the Riemann zeta function

Abstract

We show that the higher derivatives of the Riemann zeta function may be expressed in terms of integrals involving the digamma function. Related integrals for the Stieltjes constants are also shown. We also present a formula for the derivatives of the Riemann zeta function entirely in terms of the Lehmer constants.

References in corpus (5)

• On an integral involving the digamma function
• Various applications of the (exponential) complete Bell polynomials
• Some applications of the Dirichlet integrals to the summation of series and the evaluation of integrals involving the Riemann zeta function
• A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants
• Determination of the Stieltjes constants at rational arguments