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The Remainder Term of the Taylor Expansion for a Holomorphic Function Is Representable in Lagrange Form

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Abstract

We show that the remainder of the Taylor expansion for a holomorphic function can be written down in Lagrange form, provided that the argument of the function is sufficiently close to the interpolation point. Moreover, the value of the derivative in the remainder can be taken in the intersection of the disk whose diameter joins the interpolation point and the argument of the function and an arbitrary small angle whose bisectrix is the ray from the interpolation point through the argument of the function.

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Authors and Affiliations

  1. National University of Nutrition Technologies, Kiev

    E. I. Radzievskaya

  2. Institute of Mathematics, Kiev

    G. V. Radzievskii

Authors
  1. E. I. Radzievskaya
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  2. G. V. Radzievskii
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Radzievskaya, E.I., Radzievskii, G.V. The Remainder Term of the Taylor Expansion for a Holomorphic Function Is Representable in Lagrange Form. Siberian Mathematical Journal 44, 322–331 (2003). https://doi.org/10.1023/A:1022993006398

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  • DOI: https://doi.org/10.1023/A:1022993006398

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