Repeated derivatives of composite functions and generalizations of the Leibniz rule

Author(s)

Babusci, D. ^[1] ; Dattoli, G. ^[2] ; Gorska, K. ^{[3, 4, 5]} ; Penson, K. A. ^[5]

Affiliation

^[1] Ist Nazl Fis Nucl, Lab Nazl Frascati, I-00044 Rome - Italy

^[2] ENEA, Ctr Ric Frascati, I-00044 Rome - Italy

^[3] Univ Sao Paulo, Inst Fis, BR-05315970 Sao Paulo - Brazil

^[4] Polish Acad Sci, H Niewodniczanski Inst Nucl Phys, PL-31342 Krakow - Poland

^[5] Univ Paris 06, CNRS, UMR 7600, Sorbonne Univ, LPTMC, F-75252 Paris - France

• Document type: Journal article
• Source: Applied Mathematics and Computation; v. 241, p. 193-199, AUG 15 2014.
• Web of Science Citations: 1

Abstract

We use the properties of Hermite and Kampe de Feriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. These results are extended to product of functions of the above argument, thus giving rise to expressions which can formally be interpreted as generalizations of the familiar Leibniz rule. Finally, examples of practical interest are discussed. (C) 2014 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 10/15698-5 - Coherent states and semiclassical description of quantum dissipative systems, spinning systems, and quantum relativistic particles.
• Grantee: Katarzyna Górska
• Support Opportunities: Scholarships in Brazil - Post-Doctoral