Journal article
Families of Two-Point Pade Approximants and Some _4 F_3 (1)$ Identities
SIAM journal on mathematical analysis, v 26(3), pp 761-773
01 May 1995
Abstract
In this paper, a family of two-point Pade approximants, that is, two polynomials, each of degree $n$ and depending on integer $k$, $l$,$0 \leq l \leq k \leq n$, whose ratio approximates one function to order $(z^{n + l + 1} )$ at $z = 0$ and another to order $O(z^{ - n + k} )$ at $z = \infty $ is presented. The functions in question are ratios of Gaussian hypergeometric functions. Explicit closed-form expressions for the polynomials are given. Also, this derivation establishes some hypergeometric identities involving functions of the form _4 F_3 (1)$. Several interesting limiting cases, namely, $[n,n]$ and $[n - 1,n]$ Pade approximants for ratios of confluent hypergeometric functions and Bessel functions are given.
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Details
- Title
- Families of Two-Point Pade Approximants and Some _4 F_3 (1)$ Identities
- Creators
- Jet WimpBernhard Beckermann
- Publication Details
- SIAM journal on mathematical analysis, v 26(3), pp 761-773
- Publisher
- Society for Industrial and Applied Mathematics
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1995QT97500014
- Other Identifier
- 991019312439004721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied