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Some Identities of Cauchy Numbers Associated with Continued Fractions

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Abstract

In this paper, the n-th convergent of the generating function of Cauchy numbers is explicitly given. As an application, we give some new identities of Cauchy numbers in terms of binomial coefficients and harmonic numbers.

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Acknowledgements

The authors thank the referee for careful reading of the manuscript. This work has been partly done during the second author stayed in Indian Statistical Institute, New Delhi in August 2018. He thanks Professor Shanta Laishram for his kind invitation and hospitality.

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Authors and Affiliations

  1. Statistics and Mathematics Unit, Indian Statistical Institute (ISID), New Delhi, 110016, India

    Pallab Kanti Dey

  2. Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Takao Komatsu

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  1. Pallab Kanti Dey
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  2. Takao Komatsu
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Correspondence to Takao Komatsu.

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Dey, P.K., Komatsu, T. Some Identities of Cauchy Numbers Associated with Continued Fractions. Results Math 74, 83 (2019). https://doi.org/10.1007/s00025-019-1007-x

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  • DOI: https://doi.org/10.1007/s00025-019-1007-x

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