Abstract
For an integer k, define poly-Euler numbers of the second kind \(\widehat{E}_n^{(k)}\) (\(n=0,1,\ldots \)) by
When \(k=1\), \(\widehat{E}_n=\widehat{E}_n^{(1)}\) are Euler numbers of the second kind or complimentary Euler numbers defined by
Euler numbers of the second kind were introduced as special cases of hypergeometric Euler numbers of the second kind in Komatsu and Zhu (Hypergeometric Euler numbers, 2016, arXiv:1612.06210), so that they would supplement hypergeometric Euler numbers. In this paper, we study generalized Euler numbers of the second kind and give several properties and applications.
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The author thanks the anonymous referee for careful reading of the manuscript and giving the hint to Theorem 4.3.
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Komatsu, T. Complementary Euler numbers. Period Math Hung 75, 302–314 (2017). https://doi.org/10.1007/s10998-017-0199-7
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DOI: https://doi.org/10.1007/s10998-017-0199-7