Summing one- and two-dimensional series related to the Euler series

DOI10.1016/S0377-0427(98)00137-XzbMath1002.11021arXivhep-th/9801168MaRDI QIDQ1301695

Per Osland, Odd Magne Ogreid

Publication date: 16 January 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9801168

zbMATH Keywords

hypergeometric seriesRiemann zeta-functionpolylogarithmsEuler seriesFeynman diagrampsi-functionClausen function

Mathematics Subject Classification ID

Convergence and divergence of series and sequences of functions (40A30) Feynman diagrams (81T18) Other functions defined by series and integrals (33E20) Special sequences and polynomials (11B83)

Related Items (9)

Discovering and Proving Infinite Pochhammer Sum Identities ⋮ Expansion around half-integer values, binomial sums, and inverse binomial sums ⋮ Iterated binomial sums and their associated iterated integrals ⋮ Discovering and Proving Infinite Binomial Sums Identities ⋮ On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams ⋮ New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams ⋮ More series related to the Euler series. ⋮ Series involving \(\psi(z)\) and \(\zeta(z, s)\) functions and evaluation of integrals ⋮ Some infinite series related to Feynman diagrams

Cites Work

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• Some identities involving the Riemann zeta function
• Evaluation of triple Euler sums
• Explicit evaluation of Euler sums
• On an Intriguing Integral and Some Series Related to ζ(4)
• Remarks on Some Integrals and Series Involving the Stirling Numbers and ζ(n)
• The scattering of positrons by electrons with exchange on Dirac’s theory of the positron
• Space-Time Approach to Quantum Electrodynamics

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