On the Inverse of the Taylor Operator

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Published: 2025-08-08
DOI: https://doi.org/10.71712/
Keywords:
Taylor series expansion, Taylor operator, shift operator, difference operator, difference equation, Gamma function, Digamma (or Psi) function.

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Demetrios P. Kanoussis
Department of Mathematics, National Technical University of Athens, Zografu Campus, 157 80, Athens, Greece
Vassilis G. Papanicolaou
Department of Mathematics, National Technical University of Athens, Zografu Campus, 157 80, Athens, Greece

Abstract

We introduce a new expansion of a function inspired by the Taylor series expansion and we examine which functions admit such expansion. Via this expansion the solution of the difference equation \(y(x + 1) - y(x) = g(x)\) can be written down explicitly. Some examples involving the Gamma function are given.

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Vol. 24 (2013)

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Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Demetrios P. Kanoussis, & Vassilis G. Papanicolaou. (2025). On the Inverse of the Taylor Operator. Scientia Series A: Mathematical Sciences, 24, 55-66. https://doi.org/10.71712/