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On the weakened Siegel’s conjecture

Abstract

In the paper, we prove that two definitions of E-functions present in mathematics are equivalent if E-functions satisfy second-order linear differential equations. For this set of functions, a weakened variant of the well-known Siegel conjecture about representability of any E-function by a polynomial of hypergeometric functions is also proved.

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Correspondence to V. A. Gorelov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 33–39, 2005.

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Gorelov, V.A. On the weakened Siegel’s conjecture. J Math Sci 146, 5649–5654 (2007). https://doi.org/10.1007/s10958-007-0380-2

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Keywords

  • Hypergeometric Function
  • Linear Differential Equation
  • Homogeneous Equation
  • Algebraic Number
  • Laplace Transformation