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Reduction of multiple harmonic sums and harmonic polylogarithms

✍ Scribed by J. Blümlein


Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
195 KB
Volume
534
Category
Article
ISSN
0168-9002

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Harmonic sums and mellin transforms
✍ Johannes Blümlein 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 196 KB

The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions fi(x) describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories. We discuss the mathematical structure of these quantities.

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For positive integers a, b, c with a 2, let A(a, b, c) denote the triple harmonic series We show that the sum of the A(a, b, c) with a+b+c=n is `(n)= i 1 1Âi n . A similar identity for double harmonic series goes back to Euler.