Operational-umbral approach to bivariate degenerate Hermite polynomials and their partial orthogonality
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916925051764736 |
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| author | Raza, Nusrat Ahmad, Ujair Khan, Subuhi |
| author_facet | Raza, Nusrat Ahmad, Ujair Khan, Subuhi |
| contents | The operational calculus associated with special polynomials has proven to be a powerful tool for analyzing and simplifying their properties. This article examines the bivariate degenerate Hermite polynomials with a focus on their differential equations, monomiality properties, operational identities, and partial orthogonality conditions. These polynomials are redeveloped within the framework of umbral formalism, which is further extended to derive certain new results. The study concludes with key observations and insights that highlight the significance of this approach in advancing the understanding of degenerate Hermite polynomials of negative order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_21338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operational-umbral approach to bivariate degenerate Hermite polynomials and their partial orthogonality Raza, Nusrat Ahmad, Ujair Khan, Subuhi Classical Analysis and ODEs 05A40, 33C45, 35K05, 44A99 The operational calculus associated with special polynomials has proven to be a powerful tool for analyzing and simplifying their properties. This article examines the bivariate degenerate Hermite polynomials with a focus on their differential equations, monomiality properties, operational identities, and partial orthogonality conditions. These polynomials are redeveloped within the framework of umbral formalism, which is further extended to derive certain new results. The study concludes with key observations and insights that highlight the significance of this approach in advancing the understanding of degenerate Hermite polynomials of negative order. |
| title | Operational-umbral approach to bivariate degenerate Hermite polynomials and their partial orthogonality |
| topic | Classical Analysis and ODEs 05A40, 33C45, 35K05, 44A99 |
| url | https://arxiv.org/abs/2508.21338 |