A FAMILY OF MULTIPLE HARMONIC SUM AND MULTIPLE ZETA STAR VALUE IDENTITIES
نویسندگان
چکیده
منابع مشابه
New Multiple Harmonic Sum Identities
We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.
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Abstract. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler’s formula was o...
متن کاملTWO IDENTITIES FOR MULTIPLE HARMONIC q-SERIES
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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ژورنال
عنوان ژورنال: Mathematika
سال: 2014
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579313000302