ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991): 30C15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. With $s_{n} (z)$ denoting the $n$ -th partial sum of ${\rm e}^{z}$, the exact rate of convergence of the zeros of the normalized partial sums, $s_{n} (nz)$ , to the Szeg\"o curve $D_{0,\infty}$ was recently studied by Carpenter et al. (1991), where $D_{0,\infty}$ is defined by \[ D_{0,\infty} := \{ z \in {\Bbb C} : | z {\rm e}^{1-z}| = 1 {\rm \ and\ } |z| \leq 1\}. \] Here, the above results are generalized to the convergence of the zeros and poles of certain sequences of normalized Pad\'{e} approximants $R_{n,\nu} ((n+\nu)z)$ to ${\rm e}^{z}$ , where $R_{n,\nu} (z)$ is the associated Pad\'{e} rational approximation to ${\rm e}^{z}$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050055
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