The Boston Colloquium Lectures On Mathematics Delivered From September 2 to 5 1
The Boston Colloquium Lectures On Mathematics Delivered From September 2 to 5 1
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* Thus a countless manifold of continued fractions can be formed, any one of which through its convergents gives the initial series to any required number of terms and hence defines the series and table uniquely. In all of Pad&s continued fractions the partial numerators are monomials in x.
The continued fraction is called regular when its partial numer ators are all of the same degree and likewise its denominators, certain specified irregularities being admitted in the first one or two partial... fractions. These irregularities disappear when the continued fraction, as is most usual, commences with the corner element of the table. (Cf. The continued fractions (2) and (3). ) In a normal table a regular continued fraction can be obtained in any one of three ways. If we take for the convergents the approximants which fill a horizontal or vertical line, a continued fraction is obtained which except for the irregularity permitted at the outset is of the form (1) given above. If the approxi mants lie upon the principal diagonal or any parallel line, the con tinued fraction is of type (3).
What to read after The Boston Colloquium Lectures On Mathematics Delivered From September 2 to 5 1?
You can find similar books in the "Read Also" column, or choose other free books by Mass American Mathematical Society Colloquium 4th 1 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
* Thus a countless manifold of continued fractions can be formed, any one of which through its convergents gives the initial series to any required number of terms and hence defines the series and table uniquely. In all of Pad&s continued fractions the partial numerators are monomials in x.
The continued fraction is called regular when its partial numer ators are all of the same degree and likewise its denominators, certain specified irregularities being admitted in the first one or two partial... fractions. These irregularities disappear when the continued fraction, as is most usual, commences with the corner element of the table. (Cf. The continued fractions (2) and (3). ) In a normal table a regular continued fraction can be obtained in any one of three ways. If we take for the convergents the approximants which fill a horizontal or vertical line, a continued fraction is obtained which except for the irregularity permitted at the outset is of the form (1) given above. If the approxi mants lie upon the principal diagonal or any parallel line, the con tinued fraction is of type (3).
What to read after The Boston Colloquium Lectures On Mathematics Delivered From September 2 to 5 1?
You can find similar books in the "Read Also" column, or choose other free books by Mass American Mathematical Society Colloquium 4th 1 to read onlineMoreLess
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