Topic
Power series
About: Power series is a research topic. Over the lifetime, 7169 publications have been published within this topic receiving 118970 citations.
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TL;DR: For all Eichler orders with the same square-free level in a definite quaternion algebra over the field of rational numbers, this paper proved that a weighted sum of Jacobi theta series associated to these orders is a Jacobi Eisenstein series.
TL;DR: In this article , it was shown that under certain conditions integral combinations with algebraic formal power series coefficients of a U1-number in K are Um-numbers in K, where m is the degree of the algebraic extension of K(x), determined by these algebraic PRS coefficients.
Abstract: Abstract Let K be a finite field, K(x) be the field of rational functions in x over K and K be the field of formal power series over K. We show that under certain conditions integral combinations with algebraic formal power series coefficients of a U1-number in K are Um-numbers in K, where m is the degree of the algebraic extension of K(x), determined by these algebraic formal power series coefficients.
TL;DR: In this paper , the annihilating properties of polynomials and power series were studied and it was shown that for any polynomial coefficient, there exist positive integers [formula: see text] and [Formula: text] such that when the coefficients satisfy a structural equation, they are annihilated.
Abstract: In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if [Formula: see text] for polynomials [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text], whenever [Formula: see text] and [Formula: see text]. Next we prove that if [Formula: see text] for power series [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] when [Formula: see text] and [Formula: see text], [Formula: see text] for each [Formula: see text].
05 Mar 2022
TL;DR: A survey of polynomials used in power series manipulations can be found in this article , where the authors discuss the related work of De Moivre, Arbogast and Bell.
Abstract: We survey a family of polynomials that are very useful in all kinds of power series manipulations, and appearing more frequently in the literature. Applications to formal power series, generating functions and asymptotic expansions are described, and we discuss the related work of De Moivre, Arbogast and Bell.