Abstract
We introduce a full solution to a problem considered by Wang and Chu concerning series involving the squares of finite sums of the form \(1 + \frac{1}{3} + \cdots + \frac{1}{2n-1}\). Our proof involves techniques from the theory of colored multiple zeta values.
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The authors are very grateful for the referee feedback provided, which has substantially improved our article.
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All of the authors reviewed and contributed in an equal fashion to the manuscript. CX and JZ were responsible for much of the material on colored multiple zeta values and much of the material in Section 4 related to Theorem 7, and JC and PL were responsible for much of the rest of the material.
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Ce Xu is supported by the National Natural Science Foundation of China (Grant No. 12101008), the Natural Science Foundation of Anhui Province (Grant No. 2108085QA01), and the University Natural Science Research Project of Anhui Province. The corresponding Grant Number for the last case is KJ2020A0057. J. Zhao is supported by the Jacobs Prize from The Bishop’s School.
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Campbell, J.M., Levrie, P., Xu, C. et al. On a problem involving the squares of odd harmonic numbers. Ramanujan J 63, 387–408 (2024). https://doi.org/10.1007/s11139-023-00765-7
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DOI: https://doi.org/10.1007/s11139-023-00765-7