Explicit double shuffle relations and a generalization of Euler's decomposition formula

Li Guo; Bingyong Xie

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arXiv · 0808.2618

Explicit double shuffle relations and a generalization of Euler's decomposition formula

Li Guo·Bingyong Xie

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Abstract

We give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms. As an application, we generalize the well-known decomposition formula of Euler that expresses the product of two Riemann zeta values as a sum of double zeta values to a formula that expresses the product of two multiple polylogarithm values as a sum of other multiple polylogarithm values.

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Li Guo, Bingyong Xie. 2008-08-19. Explicit double shuffle relations and a generalization of Euler's decomposition formula. https://arxiv.org/abs/0808.2618

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