Numerical approximation to ζ(2n+1)

Tian-Xiao He; Michael J. Dancs

Numerical approximation to ζ(2n+1)

Tian-Xiao He, Michael J. Dancs

Illinois Wesleyan University

Research output: Journal Article › Article › peer-review

Abstract

In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.

Original language	American English
Journal	Journal of Computational and Applied Mathematics
Volume	196
State	Published - 2006

Keywords

Apery’s constant.
Bernoulli polynomial
Dirichlet series
Riemann zeta function

Disciplines

Applied Mathematics
Mathematics

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Cite this

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title = "Numerical approximation to ζ(2n+1)",

abstract = " In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.",

keywords = "Apery{\textquoteright}s constant., Bernoulli polynomial, Dirichlet series, Riemann zeta function",

author = "Tian-Xiao He and Dancs, {Michael J.}",

year = "2006",

language = "American English",

volume = "196",

journal = "Journal of Computational and Applied Mathematics",

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TY - JOUR

T1 - Numerical approximation to ζ(2n+1)

AU - He, Tian-Xiao

AU - Dancs, Michael J.

PY - 2006

Y1 - 2006

N2 - In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.

AB - In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.

KW - Apery’s constant.

KW - Bernoulli polynomial

KW - Dirichlet series

KW - Riemann zeta function

M3 - Article

VL - 196

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -