A note on harmonic number identities, Stirling series and multiple zeta values
نویسندگان
چکیده
منابع مشابه
Multiple Stirling Number Identities
A remarkable multiple analogue of the Stirling numbers of the first and second kind was recently constructed by the author. Certain summation identities, and related properties of this family of multiple special numbers are investigated in the present paper.
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Abstract. We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial coefficients. Special cases of these identities—for example, with all parameters equal to 1—have occurred in the literature. The special case with only ...
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. . . , s k are positive integers with s 1 > 1. For k ≤ n, let E(2n, k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. The well-known result E(2n, 2) = 3ζ(2n)/4was extended to E(2n, 3) and E(2n, 4) by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers E(2n, k) and then ...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2019
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304211950074x