Two-dimensional generalized gamma function and its applications
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914715337228288 |
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| author | Ponomarenko, Artem M. |
| author_facet | Ponomarenko, Artem M. |
| contents | In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later, this generalization is also a generalization the famous formula that gives the connection between the classical gamma and beta functions. Next we present properties of this generalization, some series for the generalized beta function. As a practical application of the two-dimensional generalized gamma function, we will show how it can be used to represent a fairly wide class of double integrals in the form of functional series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09711 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-dimensional generalized gamma function and its applications Ponomarenko, Artem M. General Mathematics In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later, this generalization is also a generalization the famous formula that gives the connection between the classical gamma and beta functions. Next we present properties of this generalization, some series for the generalized beta function. As a practical application of the two-dimensional generalized gamma function, we will show how it can be used to represent a fairly wide class of double integrals in the form of functional series. |
| title | Two-dimensional generalized gamma function and its applications |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2403.09711 |