Discovering and Proving Infinite Binomial Sums Identities
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Publication:2969997
DOI10.1080/10586458.2015.1116028zbMath1365.05009arXiv1507.01703OpenAlexW2963556800MaRDI QIDQ2969997
Publication date: 24 March 2017
Published in: Experimental Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1507.01703
Symbolic computation and algebraic computation (68W30) Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Higher logarithm functions (33B30) Multiple Dirichlet series and zeta functions and multizeta values (11M32)
Related Items (26)
Discovering and Proving Infinite Pochhammer Sum Identities ⋮ From Madhava–Leibniz to Lehmer’s Limit ⋮ Infinite summation formulas related to Riemann Zeta function from hypergeometric series ⋮ Hypergeometric structures in Feynman integrals ⋮ Sun's series via cyclotomic multiple zeta values ⋮ The ubiquitous Apéry number ⋮ The first-order factorizable contributions to the three-loop massive operator matrix elements \(A_{Qg}^{(3)}\) and \(\Delta A_{Qg}^{(3)}\) ⋮ Infinite series about harmonic numbers inspired by Ramanujan-like formulae ⋮ The inverse Mellin transform via analytic continuation ⋮ Logarithmic integrals with applications to BBP and Euler-type sums ⋮ Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series ⋮ Gauss's theorem and harmonic number summation formulae with certain mathematical constants ⋮ The three-loop single mass polarized pure singlet operator matrix element ⋮ General order Euler sums with multiple argument ⋮ Harmonic-binomial Euler-like sums via expansions of \((\arcsin x)^p\) ⋮ Rationalizability of square roots ⋮ Further Apéry-like series for Riemann zeta function ⋮ Explicit formulas of sums involving harmonic numbers and Stirling numbers ⋮ Alternating series of Apéry-type for the Riemann zeta function. ⋮ Unnamed Item ⋮ Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients ⋮ The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements ⋮ Proving Two Conjectural Series for $$\zeta (7)$$ and Discovering More Series for $$\zeta (7)$$ ⋮ A WZ proof for a Ramanujan-like series involving cubed binomial coefficients ⋮ Series with harmonic-like numbers and squared binomial coefficients ⋮ Nested Integrals and Rationalizing Transformations
Cites Work
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- Harmonic sums and polylogarithms generated by cyclotomic polynomials
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- Expansion around half-integer values, binomial sums, and inverse binomial sums
- Harmonic Sums, Polylogarithms,Special Numbers, and Their Generalizations
- Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms
- Single-scale diagrams and multiple binomial sums
- New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams
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