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Evaluations of some quadratic Euler sums

Ce Xu|Xin Si
대한수학회 (The Korean Mathematical Society)|2020.03|대한수학회보 (Bulletin of the KMS)|제57권 제2호|pp. 489-508|DOI 10.4134/BKMS.b190357

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참고문헌

키워드

Riemann zeta functionEuler sumHarmonic numberspolylogarithm function
주제분류수학

초록

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.

Abstract

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.

참고문헌 (21)

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