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On the decomposability of linear combinations of Bernoulli polynomials

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In the present paper we describe the complete decomposition (over \(\mathbb {C}\)) of linear combinations of the form

$$\begin{aligned} R_n(x)=B_n(x)+cB_{n-2}(x) \end{aligned}$$

of Bernoulli polynomials, where c is an arbitrary rational number.

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The authors are grateful to the referee for her/his helpful remarks.

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Correspondence to Ákos Pintér.

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Communicated by J. Schoißengeier.

Dedicated to the 75th birthday of Kálmán Győry.

Supported in part by the Hungarian Academy of Sciences, OTKA grants K100339, NK101680, NK104208 and by the European Union and the European Social Fund through project Supercomputer, the National Virtual Lab (Grant No. TÁMOP-4.2.2.C-11/1/KONV-2012-0010). This research was partially carried out in the framework of the Center of Excellence of Mechatronics and Logistics at the University of Miskolc.

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Pintér, Á., Rakaczki, C. On the decomposability of linear combinations of Bernoulli polynomials. Monatsh Math 180, 631–648 (2016).

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