Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants

DOI10.1090/S0025-5718-02-01483-7zbMath1033.11043MaRDI QIDQ4806393

Rick Kreminski

Publication date: 14 May 2003

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

Stieltjes constantsHurwitz zeta-functionLaurent expansiongeneralized Euler constantshigh precision numerical approximations

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Hurwitz and Lerch zeta functions (11M35) Evaluation of number-theoretic constants (11Y60)

Related Items (27)

Functional equations for the Stieltjes constants ⋮ New results on the Stieltjes constants: asymptotic and exact evaluation ⋮ Evaluating Fractional Derivatives of the Riemann Zeta Function ⋮ Explicit upper bounds for the Stieltjes constants ⋮ New summation relations for the Stieltjes constants ⋮ Series representations for the Stieltjes constants ⋮ A bound for Stieltjes constants ⋮ Applications of the Laurent-Stieltjes constants for Dirichlet \(L\)-series ⋮ Fast computation of the Stieltjes constants ⋮ On representations and differences of Stieltjes coefficients, and other relations ⋮ Computing Stieltjes constants using complex integration ⋮ Explicit upper bounds for the remainder term in the divisor problem ⋮ A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations ⋮ Expansions of generalized Euler's constants into the series of polynomials in \(\pi^{- 2}\) and into the formal enveloping series with rational coefficients only ⋮ The Stieltjes constants, their relation to the ηj coefficients, and representation of the Hurwitz zeta function ⋮ Approximating and bounding fractional Stieltjes constants ⋮ Addison-type series representation for the Stieltjes constants ⋮ Differentiation evens out zero spacings ⋮ Zeta Functions Over Zeros of General Zeta and L-Functions ⋮ On fractional Stieltjes constants ⋮ An efficient algorithm for the Hurwitz zeta and related functions ⋮ Unnamed Item ⋮ An effective asymptotic formula for the Stieltjes constants ⋮ An asymptotic form for the Stieltjes constants 𝛾_{𝑘}(𝑎) and for a sum 𝑆ᵧ(𝑛) appearing under the Li criterion ⋮ On the Stieltjes constants and gamma functions with respect to alternating Hurwitz zeta functions ⋮ Rigorous high-precision computation of the Hurwitz zeta function and its derivatives ⋮ Zero-free regions of the fractional derivatives of the Riemann zeta function

Cites Work

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• Using Simpson's Rule to Approximate Sums of Infinite Series
• The Stieltjes Function--Definition and Properties
• Generalized Euler constants for arithmetical progressions
• Power Series Expansions of Riemann's ζ Function
• Fractional Derivatives and Special Functions
• The Riemann zeta-function and its derivatives
• On the Hurwitz zeta-function

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