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

Joaquín Moreno, Miguel A. López, Raquel Martínez
2020 Mathematics  
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=hf(y). We apply the obtained results to solve nonlinear equations in an analytic way, and generalize Catalan and Fuss–Catalan numbers.
doi:10.3390/math8122154 fatcat:jgu2wmq5vbbmnh2jzczefrdjwm