Finite biorthogonal polynomials suggested by the finite orthogonal polynomials $M_{n}^{(p,q)}(x)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917759816826880 |
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| author | Lekesiz, Esra Güldoğan |
| author_facet | Lekesiz, Esra Güldoğan |
| contents | In this paper, we derive a pair of finite univariate biorthogonal polynomials suggested by the finite univariate orthogonal polynomials $M_{n}^{(p,q)}(x)$. The corresponding biorthogonality relation is given. Some useful relations and properties, concluding differential equation and generating function, are presented. Further, a new family of finite biorthogonal functions is obtained using Fourier transform and Parseval identity. In addition, we compute the Laplace transform and fractional calculus operators for polynomials $M_{n}(p,q,\upsilon;x)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_15010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite biorthogonal polynomials suggested by the finite orthogonal polynomials $M_{n}^{(p,q)}(x)$ Lekesiz, Esra Güldoğan Classical Analysis and ODEs In this paper, we derive a pair of finite univariate biorthogonal polynomials suggested by the finite univariate orthogonal polynomials $M_{n}^{(p,q)}(x)$. The corresponding biorthogonality relation is given. Some useful relations and properties, concluding differential equation and generating function, are presented. Further, a new family of finite biorthogonal functions is obtained using Fourier transform and Parseval identity. In addition, we compute the Laplace transform and fractional calculus operators for polynomials $M_{n}(p,q,\upsilon;x)$. |
| title | Finite biorthogonal polynomials suggested by the finite orthogonal polynomials $M_{n}^{(p,q)}(x)$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2408.15010 |