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Abstract <p> The paper considers a class of periodic <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(E\)</EquationSource> </InlineEquation>-functions for whichall derivatives at zero are integer algebraic numbers. It is shown that each such function satisfiesa differential equation of the form <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(P(y,y^{\prime })=0\)</EquationSource> </InlineEquation>(where <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(P\)</EquationSource> </InlineEquation> is a polynomial with algebraic coefficients). Asa consequence of this fact, it is proved that any such function is a Laurent polynomial in someexponential <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(e^{\alpha z}\)</EquationSource> </InlineEquation>.</p>

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On a Class of Periodic \(E \)-Functions

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. Ya. Yanchenko

摘要

Abstract

The paper considers a class of periodic \(E\) -functions for whichall derivatives at zero are integer algebraic numbers. It is shown that each such function satisfiesa differential equation of the form \(P(y,y^{\prime })=0\) (where \(P\) is a polynomial with algebraic coefficients). Asa consequence of this fact, it is proved that any such function is a Laurent polynomial in someexponential \(e^{\alpha z}\) .