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Some new expansions for certain truncated q-series

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Abstract

In this paper, we provide some new expansions for the partial sums of Euler’s pentagonal number series and Gauss’ triangular and square numbers series. As applications, inequalities between certain partition functions are established.

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Authors and Affiliations

  1. School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China

    Renrong Mao

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  1. Renrong Mao
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Correspondence to Renrong Mao.

Additional information

The author was partially supported by the National Natural Science Foundation of China (Grant No. 11501398), the Natural Science Foundation of Jiangsu Province (Grant No. BK20150304), the Natural Science Foundation for Colleges and Universities in Jiangsu Province (No. 15KJB110020), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Mao, R. Some new expansions for certain truncated q-series. Ramanujan J 46, 475–481 (2018). https://doi.org/10.1007/s11139-017-9911-8

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  • DOI: https://doi.org/10.1007/s11139-017-9911-8

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