多重调和和的结构与渐近展开

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI:10.1145/1073884.1073900

Christian Costermans, Jean-Yves Enjalbert, V. H. N. Minh, M. Petitot

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引用次数: 28

摘要

证明了多重调和和代数与洗牌代数是同构的。因此，以组合s=(s1，…，sr)为索引的多重调和和Hs作为定义在∈上的实数函数是与∈线性无关的。然后推导出多重调和和的渐近展开式算法。

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Structure and asymptotic expansion of multiple harmonic sums

We prove that the algebra of multiple harmonic sums is isomorphic to a shuffle algebra. So the multiple harmonic sums Hs, indexed by the compositions s=(s1,...,sr), are ℝ-linearly independent as real functions defined over ℕ. We deduce then the algorithm to obtain the asymptotic expansion of multiple harmonic sums.

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Proceedings of the 2005 international symposium on Symbolic and algebraic computation

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