What are some good books on continued fractions?
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What are some good books on continued fractions? [ Editor: problem statement reconstructed from the postings. ]
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Thanks to all of you who answered my request for books on continued
fractions. I thought a summary and some pertinent comments might be of
interest to some readers.
1) "Continued Fractions: Analytic Theory and Applications"
Authors: Jones and Thron (1980). Pub: Addison Wesley
Modern treatment.
2) "Seminumerical Algorithms" - Vol II of The Art of Computer
Programming. Author: Knuth. Gospers computational algorithms
and Gauss' coefficient distribution conjecture.
3) "Kettenbruchen" Author: Perron. Two volumes, in German.
Complete classical reference.
4) "Continued Fractions" Author: Wall. Analytic theory reference.
5) "Computational Complex Analysis" Author: Henrici. Analytic
theory reference.
6) "Math for Engineers ..." Authors: Bender & Orszag [Editor:
"Orzag" in the original]. Emphasis on Pade approximations.
7) "Independence in Number Theory, Physics ..." Author: Mark Kac.
AMS books (recent paperback reprint). Probabilistic theory.
8) "Ergodic Theory and Information" Author: Billingsley.
Probabilistic theory. Out of print.
9) "Continued Fractions" Author: Olds (?) Pub: Mathematical
Association of America. Suitable for high school students.
10) Title unknown. Author: A. Y. Khinchin. Pub: University of
Chicago Press (1964). Possibly a Dover reprint now.
11) "Fascinating Fractions" Author: N. M. Meskin. Pub: Mir
Publishers, Moscow. Introductory. Part of a set of short
Soviet monographs.
12) "Prime Numbers and Computer Methods [Editor: "Computational
Methods" in the original] for Factorization"
Author: Hans Riesel [Editor: "Hans Reidel" in the original].
Pub: Birkhauser (1985). See the appendix for an overview of
continued fractions.
-- Wayne K. Schroll <wayne@newton.physics.purdue.edu>
In article <1170@pur-phy> wayne@pur-phy (Wayne K. Schroll) writes:
> 3) "Kettenbruchen" Author: Perron. Two volumes, in German.
Die Lehre von den Kettenbruchen, Teubner, 1954.
> 4) "Continued Fractions" Author: Wall. Analytic theory reference.
Analytical Theory of ..., Van Nostrand, 1948
> 9) "Continued Fractions" Author: Olds (?) Pub: Mathematical
> Association of America. Suitable for high school students.
C.D. Olds. New York, Random House, 1963 (perhaps a different
book?, also elementary)
> 10) Title unknown. Author: A. Y. Khinchin. Pub: University of
> Chicago Press (1964). Possibly a Dover reprint now.
Continued Fractions (!)
> 11) "Fascinating Fractions" Author: N. M. Meskin. Pub: Mir
> Publishers, Moscow. Introductory. Part of a set of short
> Soviet monographs.
Beskin
(1986 Mir Publishers: Little Mathematics Library)
Also,
13) "The Application of Continued Fractions and Their Generalization
to Problems in Approximation Theory," A. N. Khovanskii,
Noordhoff, Groningen, 1963.
-- Victor M. Grado (School of EE, Purdue University)
[ Editor: Grado wrote his corrections under the quoted lines, with
carets pointing at the words corrected (title of 3, title of 4, the
author Olds in 9, "Title unknown" in 10, "Meskin" in 11); they are
given here after each item. ]