On the decomposability of linear combinations of Bernoulli polynomials (Q530756)
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scientific article; zbMATH DE number 6608242
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the decomposability of linear combinations of Bernoulli polynomials |
scientific article; zbMATH DE number 6608242 |
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On the decomposability of linear combinations of Bernoulli polynomials (English)
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1 August 2016
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The authors present a complete decomposition (over \(\mathbb{C}\)) of linear combinations \[ R_{n}(x)=B_{n}(x)+c B_{n-2}(x) \] of Bernoulli polynomials (where \(c \in \mathbb{Q}\)). This continues earlier work of \textit{D. Kreso} and \textit{C. Rakaczki} [Acta Arith. 161, No. 3, 267--281 (2013; Zbl 1339.11045)]. The proof depends on a careful case study based on the zeros of the derivatives of \(R_{n}(x)\).
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Bernoulli polynomials
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higher degree equations
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