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Iterated binomial sums and their associated iterated integrals - MaRDI portal

Iterated binomial sums and their associated iterated integrals (Q2934186)

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Language	Label	Description	Also known as
English	Iterated binomial sums and their associated iterated integrals	scientific article

Statements

scholarly article

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Iterated binomial sums and their associated iterated integrals (English)

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Johannes Blümlein

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Clemens G. Raab

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Carsten Schneider

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Journal of Mathematical Physics

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publication date

11 December 2014

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full work available at URL

https://arxiv.org/abs/1407.1822

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https://bib-pubdb1.desy.de/search?p=id:%22PUBDB-2015-01108%22

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zbMATH Keywords

Mellin transform

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harmonic sums

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cyclotomic sums

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describes a project that uses

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EvaluateMultiSums

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HolonomicFunctions

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MaRDI profile type

MaRDI publication profile

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Harmonic Sums, Polylogarithms,Special Numbers, and Their Generalizations

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Special values of multiple polylogarithms

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The multiple zeta value data mine

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The four-loop QCD \(\beta\)-function and anomalous dimensions

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HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS

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HARMONIC POLYLOGARITHMS

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Harmonic sums and polylogarithms generated by cyclotomic polynomials

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Nested sums, expansion of transcendental functions, and multiscale multiloop integrals

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Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

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Quasi-shuffle products

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Algebraic relations between harmonic sums and associated quantities.

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Structural relations of harmonic sums and Mellin transforms up to weight \(w=5\)

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Structural Relations of Harmonic Sums and Mellin Transforms at Weight w=6

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The third-order QCD corrections to deep-inelastic scattering by photon exchange

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The \(O(\alpha_s^3)\) massive operator matrix elements of \(O(n_f)\) for the structure function \(F_{2}(x,Q^{2})\) and transversity

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The \(O(\alpha_s^3n_fT_F^2C_{A, F})\) contributions to the gluonic massive operator matrix elements

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Massive 3-loop ladder diagrams for quarkonic local operator matrix elements

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The transition matrix element \(A_{gq}(N)\) of the variable flavor number scheme at \(O({\alpha}_s^3)\)

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The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function \(\mathrm{F}_2(\mathrm{x, Q}^{\mathrm{2}})\) and transversity

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The 3-loop pure singlet heavy flavor contributions to the structure function \(F_2(x, Q^2)\) and the anomalous dimension

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Two-loop massive operator matrix elements for unpolarized heavy flavor production to \(O(\epsilon)\)

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The \(O({\alpha}_s^2)\) heavy quark corrections to charged current deep-inelastic scattering at large virtualities

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The \(O(\alpha_s^3 T_F^2)\) contributions to the gluonic operator matrix element

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Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

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Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor-planar case

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Simplifying Multiple Sums in Difference Fields

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Central Binomial Sums, Multiple Clausen Values, and Zeta Values

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Gaussian Hypergeometric series and supercongruences

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

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New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams

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Single-scale diagrams and multiple binomial sums

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\(\overline{MS}\) vs. pole masses of gauge bosons. II: Two-loop electroweak fermion corrections

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Massive Feynman diagrams and inverse binomial sums

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Expansion around half-integer values, binomial sums, and inverse binomial sums

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Analytic continuation of Mellin transforms up to two-loop order

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Lie elements and an algebra associated with shuffles

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Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics

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The Problem of Integration in Finite Terms

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On the generalized harmonic polylogarithms of one complex variable

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Symbolic summation assists combinatorics

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Symbolic integration I: Transcendental functions

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Theory of non-commutative polynomials

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The method of differentiating under the integral sign

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An extension of Zeilberger's fast algorithm to general holonomic functions

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A fast approach to creative telescoping

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Differential rational normal forms and a reduction algorithm for hyperexponential func

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Telescopers for rational and algebraic functions via residues

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Hermite reduction and creative telescoping for hyperexponential functions

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The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates

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Summation in Finite Terms

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On solutions of linear ordinary difference equations in their coefficient field

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Solving parameterized linear difference equations in terms of indefinite nested sums and products

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SIMPLIFYING SUMS IN ΠΣ*-EXTENSIONS

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A refined difference field theory for symbolic summation

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Structural theorems for symbolic summation

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A Symbolic Summation Approach to Find Optimal Nested Sum Representations

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Parameterized telescoping proves algebraic independence of sums

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Hypergeometric solutions of linear recurrences with polynomial coefficients

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Solving difference equations in finite terms

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Determining the closed forms of the anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra

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Identifiers

zbMATH Open document ID

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10.1063/1.4900836

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2934186

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