题目：Some Formulas of Dirichlet Series
摘要: Let A be a sequence of complex numbers. In this talk we present a new family of asymptotic formulas for of digamma function of sequence A. Then we apply it and use residue theorem to obtain a new family of identities for Dirichlet series. As applications of these relations, we establish some relations of Euler sums and hyperbolic series. Moreover, we give many explicit formulas for non-alternating Euler sums with weight ≤ 6 in terms of Riemann zeta values, and for alternating Euler sums with weight ≤ 10 in terms of Riemann zeta values and polylogarithms.
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