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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 iteratif mewakili bilangan sebagai jawaban dari bagian bilangan bulatnya.[1] Bilangan bulat
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Catatan
- ↑ "Continued fraction - mathematics".
- ↑ (Pettofrezzo & Byrkit 1970, hlm. 150)
Referensi
- Siebeck, H. (1846). "Ueber periodische Kettenbrüche". J. Reine Angew. Math. Vol. 33. hlm. 68–70.
- Heilermann, J. B. H. (1846). "Ueber die Verwandlung von Reihen in Kettenbrüche". J. Reine Angew. Math. Vol. 33. hlm. 174–188.
- Magnus, Arne (1962). "Continued fractions associated with the Padé Table". Math. Z. Vol. 78. hlm. 361–374.
- Chen, Chen-Fan; Shieh, Leang-San (1969). "Continued fraction inversion by Routh's Algorithm". IEEE Trans. Circuit Theory. Vol. 16, no. 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. Vol. 4, no. 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. Vol. 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.
{{cite book}}: Ketidakcocokan ISBN / tanggal - Long, Calvin T. (1972), Elementary Introduction to Number Theory (Edisi 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 ISBN0-8284-0207-8
- 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. Vol. 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
Lihat entri pecahan berlanjut di kamus bebas Wikikamus.