Finite Bivariate Biorthogonal M-Konhauser Polynomials
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913574981468160 |
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| author | Lekesiz, Esra Güldoğan Çekim, Bayram Özarslan, Mehmet Ali |
| author_facet | Lekesiz, Esra Güldoğan Çekim, Bayram Özarslan, Mehmet Ali |
| contents | In this paper, we construct the pair of finite bivariate biorthogonal M-Konhauser polynomials, reduced to the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$, by choosing appropriate parameters in order to obtain a relation between the Jacobi Konhauser polynomials and this new finite bivariate biorthogonal polynomials $_{K}M_{n;\upsilon}^{(p,q)}(z,t)$ similar to the relation between the classical Jacobi polynomials $P_{n}^{(p,q)}(t)$ and the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$. Several properties like generating function, operational/integral representation are derived and some applications like fractional calculus, Fourier transform and Laplace transform are studied thanks to that new transition relation and the definition of finite bivariate M-Konhauser polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Bivariate Biorthogonal M-Konhauser Polynomials Lekesiz, Esra Güldoğan Çekim, Bayram Özarslan, Mehmet Ali Classical Analysis and ODEs 33C45 In this paper, we construct the pair of finite bivariate biorthogonal M-Konhauser polynomials, reduced to the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$, by choosing appropriate parameters in order to obtain a relation between the Jacobi Konhauser polynomials and this new finite bivariate biorthogonal polynomials $_{K}M_{n;\upsilon}^{(p,q)}(z,t)$ similar to the relation between the classical Jacobi polynomials $P_{n}^{(p,q)}(t)$ and the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$. Several properties like generating function, operational/integral representation are derived and some applications like fractional calculus, Fourier transform and Laplace transform are studied thanks to that new transition relation and the definition of finite bivariate M-Konhauser polynomials. |
| title | Finite Bivariate Biorthogonal M-Konhauser Polynomials |
| topic | Classical Analysis and ODEs 33C45 |
| url | https://arxiv.org/abs/2409.03355 |