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In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.
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참고문헌 (34)
참고문헌 신청
G. E. Andrews / 1999 / Special Functions, Encyclopedia of Mathematics and its Applications / Cambridge University Press :71
D. H. Bailey / 2014 / Computation and theory of extended Mordell-Tornheim-Witten sums / Math. Comp. 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
D. H. Bailey / 2014 / Computation and theory of extended Mordell-Tornheim-Witten sums / Math. Comp. 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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