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dc.creatorScott, Walter T.
dc.date.accessioned 2007-08-21T01:07:54Z
dc.date.available 2007-08-21T01:07:54Z
dc.date.issued 1938
dc.identifier.urihttps://hdl.handle.net/1911/18441
dc.description.abstract Expansion theorem. Every power series (1 · 10) C0 + C1x + C2x2+&ldots;,+Cn xn determines uniquely a continued fraction of the form (1 · 11) a0+a1x a11+a 2xa2 1+&ldots;+anx an1+&ldots; where the exponents an are positive integers and the coefficients an are complex constants. Thus any infinite set of numbers which may be regarded as the differential coefficients of a function at the origin determines uniquely a continued fraction of the form (1 · 10). This is true, in particular, of every function analytic at the origin. The continued fraction (1 · 11) is said to correspond to the power series (1 · 10) and is called a corresponding continued fraction . The power series (1 · 10) is called the corresponding power series of the continued fraction (1 · 11). There is no loss of generality in assuming that a0 = 1. The corresponding continued fraction is then (1 · 12) 1+a1xa 11+a2 xa2 1+&cdots;+an xan1+&cdots; . The continued fractions to be discussed henceforth in this paper will be of the form (1 · 12), where all of the coefficients an are different from zero. If an = 0 for some finite index n, the continued fraction is equivalent to a terminating one and represents a rational function of x.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title On continued fractions and infinite products
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation Scott, Walter T.. "On continued fractions and infinite products." (1938) Diss., Rice University. https://hdl.handle.net/1911/18441.


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