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Abstract
It is shown in a previous work that Faber-Pandharipande-Zagier’s and Miki’s identities can be derived from a polynomial identity, which in turn follows from the Fourier series expansion of sums of products of Bernoulli functions. Motivated by and generalizing this, we consider three types of functions given by sums of products of higher-order Bernoulli functions and derive their Fourier series expansions. Moreover, we express each of them in terms of Bernoulli functions.
Highlights
We recall here the following facts about the Fourier series expansion of the Bernoulli function Bn( x ): (a) for m ≥ , Bm x
5 Results and discussion It is shown in a previous work that Faber-Pandharipande-Zagier’s and Miki’s identities can be derived from a polynomial identity, which in turn follows from the Fourier series expansion of sums of products of Bernoulli functions
Motivated by and generalizing this, we consider three types of functions given by sums of products of higher-order Bernoulli functions and we obtain some new identities arising from Fourier series expansions associated with sums of products of higher-order Bernoulli functions
Summary
We recall here the following facts about the Fourier series expansion of the Bernoulli function Bn( x ): (a) for m ≥ , Bm x Bernoulli functions and find Fourier series expansions for them.
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