| dc.creator | Lampret, Vito | |
| dc.date | 2024-03-22 | |
| dc.date.accessioned | 2024-04-16T14:16:58Z | |
| dc.date.available | 2024-04-16T14:16:58Z | |
| dc.identifier | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3629 | |
| dc.identifier | 10.56754/0719-0646.2601.021 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/241518 | |
| dc.description | Asymptotic estimates for the generalized Wallis ratio \(W^*(x):=\frac{1}{\sqrt{\pi}}\cdot\frac{\Gamma(x+\frac{1}{2})}{\Gamma(x+1)}\) are presented for \(x\in\mathbb{R}^+\) on the basis of Stirling's approximation formula for the \(\Gamma\) function. For example, for an integer \(p\ge2\) and a real \(x>-\tfrac{1}{2}\) we have the following double asymptotic inequality\[A(p,x)\,<\,W^*(x)\,<\,B(p,x),\]
where\begin{align*}A(p,x):=&W_p(x)\left(1-\tfrac{1}{8(x+p)}+\tfrac{1}{128(x+p)^2}+\tfrac{1}{379(x+p)^3}\right), \\B(p,x):= &W_p(x)\left(1-\tfrac{1}{8(x+p)}+\tfrac{1}{128(x+p)^2}+\tfrac{1}{191(x+p)^3}\right),\\W_p(x):=&\frac{1}{\sqrt{\pi\,(x+p)}}\cdot\frac{(x+1)^{(p)}}{(x+\frac{1}{2})^{(p)}},\end{align*}
with \(y^{(p)}\equiv y(y+1)\cdots(y+p-1)\), the Pochhammer rising(upper) factorial of order \(p\). | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3629/2349 | |
| dc.rights | Copyright (c) 2024 V. Lampret | en-US |
| dc.rights | https://creativecommons.org/licenses/by-nc/4.0/ | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 26 No. 1 (2024); 21–32 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 26 No. 1 (2024); 21–32 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | Approximation | en-US |
| dc.subject | asymptotic | en-US |
| dc.subject | estimate | en-US |
| dc.subject | generalized Wallis’ ratio | en-US |
| dc.subject | double inequality | en-US |
| dc.subject | 26D20 | en-US |
| dc.subject | 41A60 | en-US |
| dc.subject | 11Y99 | en-US |
| dc.subject | 33E99 | en-US |
| dc.subject | 33F05 | en-US |
| dc.subject | 33B99 | en-US |
| dc.title | Double asymptotic inequalities for the generalized Wallis ratio | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
