FRACTIONAL TAYLOR EXPANSION OF CLASSICAL AND LAGUERRE-TYPE FUNCTIONS
By
Diego Caratelli¹ and Paolo Emilio Ricci²,*
¹The Antenna Company, High Tech Campus 29, 5656 AE - Eindhoven, The Netherlands & Eindhoven
University of Technology, PO Box 513, 5600 MB - Eindhoven, The Netherlands
²Mathematics Section, International Telematic University UniNettuno, Corso Vittorio Emanuele II 39, 00186 - Roma, Italia
Email: Caratelli@tue.nl, *Correspondence: paoloemilioricci@gmail.com
(Received: February 22, 2024; In format: February 24, 2024; Accepted: March 10, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54103
Abstract
Beginning with the fractional exponential, which is frequently used in applications, fractional Taylor expansions of several elementary functions in both the ordinary and Laguerrian cases are introduced, showing that some basic formulas continue to apply to new expansions. Some graphs obtained using the computer algebra system Mathematica© are given for illustration purposes.
2020 Mathematical Sciences Classification: 33C45, 11B83, 26A33.
Keywords and Phrases: Fractional exponential function, Taylor expansions in fractional powers, fractional Laguerre-type functions.