We prove that the algebra of <i>multiple harmonic sums</i> is isomorphic to a <i>shuffle algebra</i>. So the multiple harmonic sums <i>H</i><inf>s</inf>, indexed by the compositions <b>s</b>=(<i>s</i><inf>1</inf>,...,<i>s<inf>r</inf></i>), are ℝ-linearly independent as real functions defined over ℕ. We deduce then the algorithm to obtain the asymptotic… (More)
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