Bewaard in:
| Hoofdauteurs: | , |
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| Formaat: | Preprint |
| Gepubliceerd in: |
2024
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| Onderwerpen: | |
| Online toegang: | https://arxiv.org/abs/2403.05708 |
| Tags: |
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Inhoudsopgave:
- 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.