A gamma function in two variables
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2013
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| _version_ | 1866911577531219968 |
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| author | Bachraoui, Mohamed El |
| author_facet | Bachraoui, Mohamed El |
| contents | We introduce a gamma function $\Ga(x,z)$ in two complex variables which extends the classical gamma function $\Ga(z)$ in the sense that $\lim_{x\to 1}\Ga(x,z)=\Ga(z)$. We will show that many properties which $\Ga(z)$ enjoys extend in a natural way to the function $\Ga(x,z)$. Among other things we shall provide functional equations, a multiplication formula, and analogues of the Stirling formula with asymptotic estimates as consequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1305_2174 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | A gamma function in two variables Bachraoui, Mohamed El Number Theory 33B15, 11Y60, 11M06 We introduce a gamma function $\Ga(x,z)$ in two complex variables which extends the classical gamma function $\Ga(z)$ in the sense that $\lim_{x\to 1}\Ga(x,z)=\Ga(z)$. We will show that many properties which $\Ga(z)$ enjoys extend in a natural way to the function $\Ga(x,z)$. Among other things we shall provide functional equations, a multiplication formula, and analogues of the Stirling formula with asymptotic estimates as consequences. |
| title | A gamma function in two variables |
| topic | Number Theory 33B15, 11Y60, 11M06 |
| url | https://arxiv.org/abs/1305.2174 |