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${\displaystyle a_{0}+{\cfrac {1}{a_{1}+{\cfrac {1}{a_{2}+{\cfrac {1}{\ddots +{\cfrac {1}{a_{n}}}}}}}}}}$

Dalam matematika , pecahan berlanjut atau pecahan kontinu ( bahasa Inggris : Continued fraction ) adalah sebuah ekspresi yang didapat melalui proses mewakili bilangan sebagai jawaban dari nya. ^{[ 1 ]} Bilangan bulat ${\displaystyle a_{i}}$ disebut koefisien dari pecahan berlanjut. ^{[ 2 ]}

• Siebeck, H. (1846). "Ueber periodische Kettenbrüche" . J. Reine Angew. Math . 33 . hlm. 68–70.
• Heilermann, J. B. H. (1846). "Ueber die Verwandlung von Reihen in Kettenbrüche" . J. Reine Angew. Math . 33 . hlm. 174–188.
• Magnus, Arne (1962). "Continued fractions associated with the Padé Table". Math. Z . 78 . hlm. 361–374.
• Chen, Chen-Fan; Shieh, Leang-San (1969). "Continued fraction inversion by Routh's Algorithm". IEEE Trans. Circuit Theory . 16 (2). hlm. 197–202. doi : 10.1109/TCT.1969.1082925 .
• Gragg, William B. (1974). "Matrix interpretations and applications of the continued fraction algorithm". Rocky Mount. J. Math . 4 (2). hlm. 213. doi : 10.1216/RJM-1974-4-2-213 .
• Jones, William B.; Thron, W. J. (1980). Continued Fractions: Analytic Theory and Applications. Encyclopedia of Mathematics and its Applications . 11 . Reading. Massachusetts: Addison-Wesley Publishing Company. ISBN 0-201-13510-8 .
• (1964) [Originally published in Russian, 1935]. Continued Fractions . University of Chicago Press . ISBN 0-486-69630-8 .
• Long, Calvin T. (1972), Elementary Introduction to Number Theory (edisi ke-2nd), Lexington: , LCCN 77-171950
• (1950). Die Lehre von den Kettenbrüchen . New York, NY: Chelsea Publishing Company.
• Pettofrezzo, Anthony J.; Byrkit, Donald R. (1970), Elements of Number Theory , Englewood Cliffs: Prentice Hall , LCCN 77-81766
• Rockett, Andrew M.; Szüsz, Peter (1992). Continued Fractions . World Scientific Press. ISBN 981-02-1047-7 .
• H. S. Wall, Analytic Theory of Continued Fractions , D. Van Nostrand Company, Inc., 1948 ISBN 0-8284-0207-8
• Cuyt, A.; Brevik Petersen, V.; Verdonk, B.; Waadeland, H.; Jones, W. B. (2008). Handbook of Continued fractions for Special functions . Springer Verlag. ISBN 978-1-4020-6948-2 .
• Rieger, G. J. (1982). "A new approach to the real numbers (motivated by continued fractions)". Abh. Braunschweig.Wiss. Ges . 33 . hlm. 205–217.

• Hazewinkel, Michiel , ed. (2001) [1994], , Encyclopedia of Mathematics , Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
• An Introduction to the Continued Fraction
• Linas Vepstas Continued Fractions and Gaps (2004) reviews chaotic structures in continued fractions.
• Continued Fractions on the Stern-Brocot Tree at
• The Antikythera Mechanism I: Gear ratios and continued fractions
• Continued fraction calculator , WIMS.
• Continued Fraction Arithmetic Gosper's first continued fractions paper, unpublished. Cached on the Internet Archive 's Wayback Machine
• (Inggris) Weisstein, Eric W. "Continued Fraction" . MathWorld .
• Continued Fractions by Stephen Wolfram and Continued Fraction Approximations of the Tangent Function by Michael Trott, .
• A view into "fractional interpolation" of a continued fraction {1; 1, 1, 1, ... }
• Best rational approximation through continued fractions