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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-06-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2025-0133 |
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| Summary: | 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. |
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| ISSN: | 2391-4661 |