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

2009/02/10 by Donal F. Connon, Connon, Donal F. · 2 citations
Mathematics · Physics and Astronomy · #11M06 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0902.1691

openalex publication_date 2009/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Positivity of a Sequence of Numbers and the Riemann Hypothesis

Cited by

• The difference between two Stieltjes constants
• Some integrals involving the Stieltjes constants:Part II

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