Convergence of ray sequences of Pade approximants to 2F1(a,1;c;z), c>a>0
| dc.creator | Driver, K | |
| dc.creator | Jordaan, K | |
| dc.date | 2009-01-05 | |
| dc.date.accessioned | 2026-07-07T12:24:34Z | |
| dc.date.available | 2026-07-07T12:24:34Z | |
| dc.description | The Padé table of $\phantom{}_2F_1(a,1;c;z)$ is normal for $c>a>0$ (cf. \cite{3}). For $m \geq n-1$ and $c \notin {\zz}^{\phantom{}^-}$, the denominator polynomial $Q_{mn}(z)$ in the $[m/n]$ Padé approximant $P_{mn}(z)/Q_{mn}(z)$ for $\phantom{}_2F_1(a,1;c;z)$ and the remainder term $Q_{mn}(z)\phantom{}_2F_1(a,1;c;z)-P_{mn}(z)$ were explicitly evaluated by Padé (cf. \cite{2}, \cite{5} or \cite{7}). We show that for $c>a>0$ and $m\geq n-1$, the poles of $P_{mn}(z)/Q_{mn}(z)$ lie on the cut $(1,\infty)$. We deduce that the sequence of approximants $P_{mn}(z)/Q_{mn}(z)$ converges to $\phantom{}_2F_1(a,1;c;z)$ as $m \to \infty$, $ n/m \to ρ$ with $0<ρ\leq 1$, uniformly on compact subsets of the unit disc $|z|<1$ for $c>a>0$ | |
| dc.identifier | https://arxiv.org/abs/0901.0435 | |
| dc.identifier | http://arxiv.org/abs/0901.0435 | |
| dc.identifier | Quaestiones Mathematicae, 25 (2002), 1-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214364 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 41A21; 30E15 | |
| dc.title | Convergence of ray sequences of Pade approximants to 2F1(a,1;c;z), c>a>0 | |
| dc.type | text |