Analytic Theory of Continued Fractions (eBook)

Hubert Stanley Wall (1902–71) received his Ph.D. from the University of Wisconsin. He taught at Northwestern and the Illinois Institute of Technology before joining the faculty of the University of Texas at Austin in 1946, where he spent the rest of his career and supervised more than 60 mathematics doctoral students.

PrefaceIntroductionChapter I: The Continued Fraction as a Product of Linear Fractional Transformations.Chapter II: Convergence Theorems.Chapter III: Convergence of Continued Fractions Whose Partial Denominators are Equal to Unity.Chapter IV: Introduction to the Theory of Positive Definite Continued Fractions.Chapter V: Some General Convergence Theorems.Chapter VI: Stieltjes Type Continued Fractions.Chapter VII: Extensions of the Parabola Theorem.Chapter VIII: The Value Region Theorem.Chapter IX: J-Fraction Expansions for Rational Functions.Chapter X: Theory of Equations.Chapter XI: J-Fraction Expansions for Power Series.Chapter XII: Matrix Theory of Continued Fractions.Chapter XIII: Continued Fractions and Definite Integrals.Chapter XIV: The Moment Problem For a Finite Interval.Chapter XV: Bounded Analytic Functions.Chapter XVI: Hausdorff Summability.Chapter XVII: The Moment Problem For an Infinite Interval.Chapter XVIII: The Continued Fraction of Gauss.Chapter XIX: The Stieltjes Summability.Chapter XX: The Pade Table. (e in Pade needs acute accent)Bibliography.Index.