منابع مشابه
Algorithms for Some Euler-Type Identities for Multiple Zeta Values
. . . , 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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This paper is devoted to a systematic study of combinatorial identities which assert the equality of different sets of compositions, or ordered partitions, of integers. The proofs are based on properties of zig-zag graphs the graphical representations of compositions introduced by Percy A. MacMahon in his classic book Combinatory Analysis. In particular it is demonstrated, by means of general t...
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The constant is the best possible. There is a vast literature which deals with alternative proofs, various generalizations and extensions, and numerous variants and applications in analysis of inequality (1.1); see [1, 2, 3, 5, 7, 9, 8, 10, 13, 14, 15, 16, 17, 18, 19] and the references given therein. According to Hardy (see [6, Theorem 349]), Carleman’s inequality was generalized as follows. I...
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ژورنال
عنوان ژورنال: Acta Universitatis Sapientiae, Mathematica
سال: 2016
ISSN: 2066-7752
DOI: 10.1515/ausm-2016-0007