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This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.
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참고문헌 (21)
참고문헌 신청
G. E. Andrews / 1999 / Special functions / Cambridge University Press
David H. Bailey / 2014 / Computation and theory of extended Mordell-Tornheim-Witten sums / Mathematics of Computation 83(288):1795~1821
D. H. Bailey / 1994 / Experimental evaluation of Euler sums / Experiment. Math 3(1):17~30
B. C. Berndt / 1985 / Ramanujan's Notebooks. Part I / Springer-Verlag
B. C. Berndt / 1989 / Ramanujan's Notebooks. Part II / Springer-Verlag
David H. Bailey / 2014 / Computation and theory of extended Mordell-Tornheim-Witten sums / Mathematics of Computation 83(288):1795~1821
D. H. Bailey / 1994 / Experimental evaluation of Euler sums / Experiment. Math 3(1):17~30
B. C. Berndt / 1985 / Ramanujan's Notebooks. Part I / Springer-Verlag
B. C. Berndt / 1989 / Ramanujan's Notebooks. Part II / Springer-Verlag
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