Orthogonalizing q-Bernoulli polynomials
In this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called OBn(x,q){{\rm{OB}}}_{n}(x,q) from the q-Bernoulli polynomials. We demonstrate the relationship between polynomials OBn(x,q){{\rm{OB}}}_{n}(x,q) and the little q-Legendre polyno...
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De Gruyter
2025-06-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2025-0133 |
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| author | Kuş Semra Tuglu Naim |
| author_facet | Kuş Semra Tuglu Naim |
| author_sort | Kuş Semra |
| collection | DOAJ |
| description | In this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called OBn(x,q){{\rm{OB}}}_{n}(x,q) from the q-Bernoulli polynomials. We demonstrate the relationship between polynomials OBn(x,q){{\rm{OB}}}_{n}(x,q) and the little q-Legendre polynomials, and derive a generalized formula for OBn(x,q){{\rm{OB}}}_{n}(x,q) by leveraging the little q-Legendre polynomials. Furthermore, we present some properties of polynomials OBn(x,q){{\rm{OB}}}_{n}(x,q). Finally, we introduce a hybrid of block-pulse function and orthogonal polynomials OBn(x,q){{\rm{OB}}}_{n}(x,q) and examine various properties of these polynomials. |
| format | Article |
| id | doaj-art-14b4439bc6fa40d1b012a4e5826ff1bd |
| institution | Kabale University |
| issn | 2391-4661 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-14b4439bc6fa40d1b012a4e5826ff1bd2025-08-20T03:24:51ZengDe GruyterDemonstratio Mathematica2391-46612025-06-0158191810.1515/dema-2025-0133Orthogonalizing q-Bernoulli polynomialsKuş Semra0Tuglu Naim1Mucur Vocational High School, Kırşehir Ahi Evran University, Kırşehir, TurkeyDepartment of Mathematics, Faculty of Science, Gazi University, Teknikokullar 06500, Ankara, TurkeyIn this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called OBn(x,q){{\rm{OB}}}_{n}(x,q) from the q-Bernoulli polynomials. We demonstrate the relationship between polynomials OBn(x,q){{\rm{OB}}}_{n}(x,q) and the little q-Legendre polynomials, and derive a generalized formula for OBn(x,q){{\rm{OB}}}_{n}(x,q) by leveraging the little q-Legendre polynomials. Furthermore, we present some properties of polynomials OBn(x,q){{\rm{OB}}}_{n}(x,q). Finally, we introduce a hybrid of block-pulse function and orthogonal polynomials OBn(x,q){{\rm{OB}}}_{n}(x,q) and examine various properties of these polynomials.https://doi.org/10.1515/dema-2025-0133q-bernoulli polynomialsorthonormal polynomialsblock-pulse functions33c4511b68 |
| spellingShingle | Kuş Semra Tuglu Naim Orthogonalizing q-Bernoulli polynomials Demonstratio Mathematica q-bernoulli polynomials orthonormal polynomials block-pulse functions 33c45 11b68 |
| title | Orthogonalizing q-Bernoulli polynomials |
| title_full | Orthogonalizing q-Bernoulli polynomials |
| title_fullStr | Orthogonalizing q-Bernoulli polynomials |
| title_full_unstemmed | Orthogonalizing q-Bernoulli polynomials |
| title_short | Orthogonalizing q-Bernoulli polynomials |
| title_sort | orthogonalizing q bernoulli polynomials |
| topic | q-bernoulli polynomials orthonormal polynomials block-pulse functions 33c45 11b68 |
| url | https://doi.org/10.1515/dema-2025-0133 |
| work_keys_str_mv | AT kussemra orthogonalizingqbernoullipolynomials AT tuglunaim orthogonalizingqbernoullipolynomials |