Orthogonalizing q -Bernoulli polynomials
Year: 2025
Type: article
Abstract: In this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called OB n ( x , q ) {{\rm{OB}}}_{n}(x,q) from the q -Bernoulli polynomials. We demonstrate the relationship between polynomials OB n ( x , q ) {{\rm{OB}}}_{n}(x,q) and the little q -Legendre polynomials, and derive a generalized formula for OB n ( x , q ) {{\rm{OB}}}_{n}(x,q) by leveraging the little q -Legendre polynomials. Furthermore, we present some properties of polynomials OB n ( x , q ) {{\rm{OB}}}_{n}(x,q) . Finally, we introduce a hybrid of block-pulse function and orthogonal polynomials OB n ( x , q ) {{\rm{OB}}}_{n}(x,q) and examine various properties of these polynomials.
Source: Demonstratio Mathematica
Authors: Semra Kuş, Naim Tuglu
Institutions: Ahi Evran University, Gazi University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4411734725