The Padé approximant technique has emerged as a powerful mathematical aid for treating certain physical problems. Often, however, students are not aware of the technique or its uses. A grasp of the method can be obtained from the continued fraction approach, which in one aspect is a subset of the Padé technique. Continued fractions and the more familiar power series method both depend on an unknown remainder term. The quantitative difference is that for many functions, the dependence of the continued fraction on the remainder term is very slight. This paper illustrates the continued fraction approach, mainly by example. Two idealized versions of quite different physical problems are first treated. Then the technique is applied to a numerical example and finally, to a more mathematical type of question.
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May 01 1978
Padé approximants via the continued fraction approach
J. Sullivan
J. Sullivan
Center for Experiment Design and Data Analysis, Environmental Data Service, National Oceanic and Atmospheric Administration, Washington, D.C. 20235
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Am. J. Phys. 46, 489–494 (1978)
Citation
J. Sullivan; Padé approximants via the continued fraction approach. Am. J. Phys. 1 May 1978; 46 (5): 489–494. https://doi.org/10.1119/1.11241
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