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Algorithms for Some Euler-Type Identities for Multiple Zeta Values

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  • Shifeng Ding
  • Weijun Liu

Abstract

Multiple zeta values are the numbers defined by the convergent series , where , , , are positive integers with . For , let be the sum of all multiple zeta values with even arguments whose weight is and whose depth is . The well-known result was extended to and by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers and then gave a direct formula for for arbitrary . In this paper we apply a technique introduced by Granville to present an algorithm to calculate and prove that the direct formula can also be deduced from Eisenstein's double product.

Suggested Citation

  • Shifeng Ding & Weijun Liu, 2013. "Algorithms for Some Euler-Type Identities for Multiple Zeta Values," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, February.
    • Handle: RePEc:hin:jnljam:802791
    DOI: 10.1155/2013/802791
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