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Abstract

Applying the theory of modular forms and Lambert series manipulations we establish an Eisenstein series identity. From this formula we confirm a Lambert series identity conjectured by Gosper. Another Lambert series identity of Gosper is also confirmed by using Lambert series manipulations.

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References

  1. Gosper, R.W.: Experiments and discoveries in \(q\)-trigonometry. In: Garvan, F.G., Ismail, M.E.H. (eds.) Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, pp. 79–105. Kluwer, Springer (2001)

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant No. 11801451) and the Natural Science Foundation of Hunan Province (Grant No. 2020JJ5682).

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Correspondence to Bing He.

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He, B. Proofs for two Lambert series identities of Gosper . RACSAM 115, 136 (2021). https://doi.org/10.1007/s13398-021-01076-6

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  • DOI: https://doi.org/10.1007/s13398-021-01076-6

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