Pecahan berlanjut

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Dalam matematika, pecahan berlanjut atau pecahan kontinu (bahasa Inggris: Continued fraction) adalah sebuah ekspresi yang didapat melalui proses iteratif mewakili bilangan sebagai jawaban dari bagian bilangan bulatnya. Bilangan bulat $a_{i}$ disebut koefisien dari pecahan berlanjut.

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

Referensi

• 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. 
• Khinchin, A. Ya. (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: D. C. Heath and Company, LCCN 77-171950 
• Perron, Oskar (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. 

Pranala luar

• Hazewinkel, Michiel, ed. (2001) [1994], "Continued fraction", 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 cut-the-knot
• 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, Wolfram Demonstrations Project.
• Templat:OEIS el
• A view into "fractional interpolation" of a continued fraction {1; 1, 1, 1, ...}
• Best rational approximation through continued fractions