Sábháilte in:
| Príomhchruthaitheoirí: | , |
|---|---|
| Formáid: | Preprint |
| Foilsithe / Cruthaithe: |
2024
|
| Ábhair: | |
| Rochtain ar líne: | https://arxiv.org/abs/2403.05708 |
| Clibeanna: |
Cuir clib leis
Níl clibeanna ann, Bí ar an gcéad duine le clib a chur leis an taifead seo!
|
| _version_ | 1866913260140232704 |
|---|---|
| author | Karp, Dmitrii Kuznetsov, Alexey |
| author_facet | Karp, Dmitrii Kuznetsov, Alexey |
| contents | By replacing the Euler gamma function by the Barnes double gamma function in the definition of the Meijer $G$-function, we introduce a new family of special functions, which we call $K$-functions. This is a very general class of functions, which includes as special cases Meijer $G$-functions (thus also all hypergeometric functions ${}_p F_q$) as well as several new functions that appeared recently in the literature. Our goal is to define the $K$-function, study its analytic and transformation properties and relate it to several functions that appeared recently in the study of random processes and the fractional Laplacian. We further introduce a generalization of the Kilbas-Saigo function and show that it is a special case of $K$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05708 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extending the Meijer $G$-function Karp, Dmitrii Kuznetsov, Alexey Classical Analysis and ODEs Complex Variables 33C60, 33B15 By replacing the Euler gamma function by the Barnes double gamma function in the definition of the Meijer $G$-function, we introduce a new family of special functions, which we call $K$-functions. This is a very general class of functions, which includes as special cases Meijer $G$-functions (thus also all hypergeometric functions ${}_p F_q$) as well as several new functions that appeared recently in the literature. Our goal is to define the $K$-function, study its analytic and transformation properties and relate it to several functions that appeared recently in the study of random processes and the fractional Laplacian. We further introduce a generalization of the Kilbas-Saigo function and show that it is a special case of $K$-function. |
| title | Extending the Meijer $G$-function |
| topic | Classical Analysis and ODEs Complex Variables 33C60, 33B15 |
| url | https://arxiv.org/abs/2403.05708 |