ON THE LANCZOS ORTHOGONAL DERIVATIVE

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 92

Volume : 19 , Issue : 3
DOI: https://doi.org/10.56827/SEAJMMS.2023.1903.3
Author :
J. D. Bulnes (Departamento de Ciencias Exatas e Tecnología, Universidade Federal do Amapa, Rod. Juscelino Kubitschek Jardin Marco Zero, 68903-419, Macapa, AP, BRASI)
J. López-Bonilla (ESIME-Zacatenco, Instituto Politecnico Nacional Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, MEXICO)
R. Rajendra (Department of Mathematics, Field Marshal K.M. Cariappa College, Mangalore University, Madikeri-571 201, INDIA)
P. Siva Kota Reddy (Department of Mathematics, Sri Jayachamarajendra College of Engineering, JSS Science and Technology University, Mysuru-570 006, INDIA)

Abstract

We use the Kempf et al. (2014 $\&$ 2015) process of integration by differentiation to obtain the Lanczos generalized derivative, and we give a simple deduction of the Rangarajan–Purushothaman’s formula for the orthogonal derivative for higher orders. Besides, we show that the Lanczos derivative allows deduce an interesting algebraic expression for the first derivative of a function.

Keywords and Phrases

Differentiation by integration, Integration by differentiation, Lanczos derivative, Legendre polynomials, Orthogonal derivative.

A.M.S. subject classification

26A24, 26A42, 33C45, 65D25.

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