The Q-D algorithm for transforming series expansions into a corresponding continued fractions: An extension to cope with zero coefficients

EXL De Andrade; John Henry McCabe; A Sri Ranga

doi:10.1016/S0377-0427(03)00389-3

The Q-D algorithm for transforming series expansions into a corresponding continued fractions: An extension to cope with zero coefficients

EXL De Andrade
, John Henry McCabe
, A Sri Ranga

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

An algorithm for deriving a continued fraction that corresponds to two series expansions simultaneously, when there are zero coefficients in one or both series, is given. It is based on using the Q-D algorithm to derive the corresponding fraction for two related series, and then transforming it into the required continued fraction. Two examples are given. (C) 2003 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	487-497
Number of pages	11
Journal	Journal of Computational and Applied Mathematics
Volume	156
Issue number	2
DOIs	https://doi.org/10.1016/S0377-0427(03)00389-3
Publication status	Published - 15 Jul 2003

Keywords

continued fractions
Pade approximants

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title = "The Q-D algorithm for transforming series expansions into a corresponding continued fractions: An extension to cope with zero coefficients",

abstract = "An algorithm for deriving a continued fraction that corresponds to two series expansions simultaneously, when there are zero coefficients in one or both series, is given. It is based on using the Q-D algorithm to derive the corresponding fraction for two related series, and then transforming it into the required continued fraction. Two examples are given. (C) 2003 Elsevier B.V. All rights reserved.",

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AU - De Andrade, EXL

AU - McCabe, John Henry

AU - Sri Ranga, A

PY - 2003/7/15

Y1 - 2003/7/15

N2 - An algorithm for deriving a continued fraction that corresponds to two series expansions simultaneously, when there are zero coefficients in one or both series, is given. It is based on using the Q-D algorithm to derive the corresponding fraction for two related series, and then transforming it into the required continued fraction. Two examples are given. (C) 2003 Elsevier B.V. All rights reserved.

AB - An algorithm for deriving a continued fraction that corresponds to two series expansions simultaneously, when there are zero coefficients in one or both series, is given. It is based on using the Q-D algorithm to derive the corresponding fraction for two related series, and then transforming it into the required continued fraction. Two examples are given. (C) 2003 Elsevier B.V. All rights reserved.

KW - continued fractions

KW - Pade approximants

U2 - 10.1016/S0377-0427(03)00389-3

DO - 10.1016/S0377-0427(03)00389-3

M3 - Article

SN - 0377-0427

VL - 156

SP - 487

EP - 497

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

The Q-D algorithm for transforming series expansions into a corresponding continued fractions: An extension to cope with zero coefficients

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Keywords

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