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A two-sided Faulhaber-like formula involving Bernoulli polynomials

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URI: https://hdl.handle.net/10016/32262
ISSN: 1631-073X
DOI: https://doi.org/10.5802/crmath.10
UXXI: AR/0000024704
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two-sided_CRM_2020.pdf (479.07 KB)
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2020-03-19
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Académie des Sciences, Paris
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Abstract
We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in particular, a Faulhaber-like formula for sums of the form 1m(n−1)m+2m(n−2)m+⋯+(n−1)m1m for positive integers m and n.
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Bernoulli polynomials, Faulhaber formula
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Barbero G., J.F., Margalef-Bentabol, J. and Villaseñor, E.J.S. (2020). A two-sided Faulhaber-like formula involving Bernoulli polynomials. Comptes Rendus Mathématique, 358(1), pp. 41-44
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