Version 1
: Received: 25 February 2023 / Approved: 27 February 2023 / Online: 27 February 2023 (06:44:12 CET)
How to cite:
Amiri, M. A Theorem on Separated Transformations of Basis Vectors of Polynomial Space and Its Applications in Special Polynomials and Related Lie Algebra. Preprints2023, 2023020450. https://doi.org/10.20944/preprints202302.0450.v1
Amiri, M. A Theorem on Separated Transformations of Basis Vectors of Polynomial Space and Its Applications in Special Polynomials and Related Lie Algebra. Preprints 2023, 2023020450. https://doi.org/10.20944/preprints202302.0450.v1
Amiri, M. A Theorem on Separated Transformations of Basis Vectors of Polynomial Space and Its Applications in Special Polynomials and Related Lie Algebra. Preprints2023, 2023020450. https://doi.org/10.20944/preprints202302.0450.v1
APA Style
Amiri, M. (2023). A Theorem on Separated Transformations of Basis Vectors of Polynomial Space and Its Applications in Special Polynomials and Related Lie Algebra. Preprints. https://doi.org/10.20944/preprints202302.0450.v1
Chicago/Turabian Style
Amiri, M. 2023 "A Theorem on Separated Transformations of Basis Vectors of Polynomial Space and Its Applications in Special Polynomials and Related Lie Algebra" Preprints. https://doi.org/10.20944/preprints202302.0450.v1
Abstract
The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
