On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira
type: Item
instance of: scholarly article
title: On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira
zbMATH Open document ID: 0744.30003
DOI: 10.1155/S0161171290000941
author: L. M. B. C. Campos
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/46677
review text: In this paper an extension is given of the classical theorems of Taylor, Lagrange, Laurent and Teixeira. The function \(F(z)\), which is analytic or has an isolated singularity at a point \(z=a\), is replaced by its derivative of complex order \(F^{(\nu)}(z)\) in a sense. The series representations of \(F^{(\nu)}(z)\) are involved with non-integral powers coming from fractional derivatives or integrals. As an application, generating functions are established for the Hermite and Bessel functions with complex parameters.
Mathematics Subject Classification ID: 30B50
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 9364
zbMATH Keywords: fractional derivatives
zbMATH Keywords: generalized Taylor series
zbMATH Keywords: generalized Laurent series
zbMATH Keywords: generating functions
zbMATH Keywords: Bessel functions
zbMATH Keywords: Hermite functions
reviewed by: Ekkehard Krätzel
MaRDI profile type: Publication
OpenAlex ID: W2001047822
description: scientific article; zbMATH DE number 9364