On Bivariate Jacobi Konhauser Polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912032734838784 |
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| author | Özarslan, Mehmet Ali Elidemir, İlkay Onbaşı |
| author_facet | Özarslan, Mehmet Ali Elidemir, İlkay Onbaşı |
| contents | Recently, Özarslan and Elidemir (2023) introduced a methodology for constructing two-variable biorthogonal polynomial families with the help of one-variable biorthogonal and orthogonal polynomial families. The primary objective of the paper is to introduce novel class of two-variable biorthogonal polynomials namley bivariate Jacobi Konhauser polynomials. We investigate several fundamental properties of these polynomials including their biorthogonality property, operational formula, generating function, and integral representation. Furthermore, We inverstigate their images under the Laplace transform, fractional integral and derivative operators. Corresponding to these polynomials, we define the new type bivariate Jacobi Konhauser Mittag Leffler (JKML) function and obtain the similar properties for them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Bivariate Jacobi Konhauser Polynomials Özarslan, Mehmet Ali Elidemir, İlkay Onbaşı Classical Analysis and ODEs 33C50, 26A33, 44A20 Recently, Özarslan and Elidemir (2023) introduced a methodology for constructing two-variable biorthogonal polynomial families with the help of one-variable biorthogonal and orthogonal polynomial families. The primary objective of the paper is to introduce novel class of two-variable biorthogonal polynomials namley bivariate Jacobi Konhauser polynomials. We investigate several fundamental properties of these polynomials including their biorthogonality property, operational formula, generating function, and integral representation. Furthermore, We inverstigate their images under the Laplace transform, fractional integral and derivative operators. Corresponding to these polynomials, we define the new type bivariate Jacobi Konhauser Mittag Leffler (JKML) function and obtain the similar properties for them. |
| title | On Bivariate Jacobi Konhauser Polynomials |
| topic | Classical Analysis and ODEs 33C50, 26A33, 44A20 |
| url | https://arxiv.org/abs/2405.15043 |