On Recurrence Relations for the Extensions of Euler Sums
نویسندگان
چکیده
منابع مشابه
Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums
We show that integrals of the form ∫ 1 0 xLip(x)Liq(x)dx (m ≥ −2, p, q ≥ 1) and ∫ 1 0 log(x)Lip(x)Liq(x) x dx (p, q, r ≥ 1) satisfy certain recurrence relations which allow us to write them in terms of Euler sums. From this we prove that, in the first case for all m, p, q and in the second case when p+ q+ r is even, these integrals are reducible to zeta values. In the case of odd p+q+r, we comb...
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Abstract. In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, Derivation and double shuffle relations for multiple zeta values. Compos. Math. 142 (2)(2006), 307–338). After setting up the general framework we provide some numerical evidence for our two main conjectures. At the ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2008
ISSN: 0035-7596
DOI: 10.1216/rmj-2008-38-1-225