On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams

DOI10.1016/j.cam.2005.01.003zbMath1134.33304arXivmath-ph/0505051OpenAlexW2110545326MaRDI QIDQ2488288

Mark W. Coffey

Publication date: 25 August 2005

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

Full work available at URL: https://arxiv.org/abs/math-ph/0505051

zbMATH Keywords

Hurwitz zeta functionRiemann zeta functionEuler sumsGamma functionClausen functionHypergeometric functionDigamma functionHarmonic numbersPolylogarithm functionDilogarithm functionPolygamma functionTrilogarithm function

Mathematics Subject Classification ID

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Other functions defined by series and integrals (33E20) Higher logarithm functions (33B30)

Related Items (21)

Towards the one-loop Kähler metric of Calabi-Yau orientifolds ⋮ Some monotonicity properties and inequalities for the generalized digamma and polygamma functions ⋮ Monotonic properties for ratio of the generalized (p,k)-polygamma functions ⋮ Identities for alternating inverse squared binomial and harmonic number sums ⋮ On harmonic numbers and nonlinear Euler sums ⋮ Inequalities for the inverses of the polygamma functions ⋮ Series representations for the Apéry constant \(\zeta (3)\) involving the values \(\zeta (2n)\) ⋮ Identities on harmonic and \(q\)-harmonic number sums ⋮ Euler sums of generalized harmonic numbers and connected extensions ⋮ Complete monotonicity related to the \(k\)-polygamma functions with applications ⋮ Monotonicity, concavity, and inequalities related to the generalized digamma function ⋮ On \(q\)-analogues of quadratic Euler sums ⋮ New families of alternating harmonic number sums ⋮ On representation problems of Euler sums with multi-parameters ⋮ Harmonic-number summation identities, symmetric functions, and multiple zeta values ⋮ Combinatorial identities involving harmonic numbers ⋮ On generalized harmonic number sums ⋮ Hypergeometric summation representations of the Stieltjes constants ⋮ Harmonic sums and polylogarithms generated by cyclotomic polynomials ⋮ Quadratic alternating harmonic number sums ⋮ Integral and series representations of the digamma and polygamma functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Clausen integral \(Cl_ 2(\theta)\) and a related integral
• Formulae concerning the computation of the Clausen integral \(Cl_ 2(\theta)\)
• A formula of S. Ramanujan
• On some series containing \(\psi{}(x)-\psi{}(y)\) and \((\psi{}(x)- \psi{}(y))^ 2\) for certain values of \(x\) and \(y\)
• The Riemann zeta-function. Transl. from the Russian by Neal Koblitz
• Summing one- and two-dimensional series related to the Euler series
• On some log-cosine integrals related to \(\zeta(3), \zeta(4)\), and \(\zeta(6)\).
• Some infinite series related to Feynman diagrams
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Central Binomial Sums, Multiple Clausen Values, and Zeta Values
• Euler Sums and Contour Integral Representations
• HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS
• Experimental Evaluation of Euler Sums
• Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums
• Explicit evaluation of Euler sums
• On an Intriguing Integral and Some Series Related to ζ(4)
• More series related to the Euler series.

This page was built for publication: On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams