Explicit Construction of the Inverse of an Analytic Real Function: Some Applications

Joaquín Moreno, Miguel A. López and Raquel Martínez
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Joaquín Moreno: Department of Applied Mathematics, Superior Technical School of Building Engineering, Polytechnic University of Valencia, 46022 Valencia, Spain
Miguel A. López: SIDIS Research Group, Department of Mathematics and Institute of Applied Mathematics in Science and Engineering (IMACI), Polytechnic School of Cuenca, University of Castilla-La Mancha, 16071 Cuenca, Spain
Raquel Martínez: SIDIS Research Group, Department of Mathematics and Institute of Applied Mathematics in Science and Engineering (IMACI), Polytechnic School of Cuenca, University of Castilla-La Mancha, 16071 Cuenca, Spain

Mathematics, 2020, vol. 8, issue 12, 1-23

Abstract: In this paper, we introduce a general procedure to construct the Taylor series development of the inverse of an analytical function; in other words, given y = f ( x ) , we provide the power series that defines its inverse x = h f ( y ) . We apply the obtained results to solve nonlinear equations in an analytic way, and generalize Catalan and Fuss–Catalan numbers.

Keywords: inverse functions; Taylor series; Taylor Remainder; nonlinear equations; Catalan numbers; Fuss–Catalan numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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