Lihat sumber Pecahan berlanjut

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Dalam [[matematika]], '''pecahan berlanjut''' adalah sebuah [[ekspresi (matematika)|ekspresi]] yang didapat melalui proses [[iteratif]] mewakili bilangan sebagai jawaban dari [[bagian integer]]nya.<ref>{{cite web|url=http://www.britannica.com/EBchecked/topic/135043/continued-fraction|title=Continued fraction - mathematics|publisher=}}</ref> Integer <math>a_i</math> disebut [[koefisien]] dari pecahan berlanjut.<ref name="Pettofrezzo 1970 150">{{harvtxt|Pettofrezzo|Byrkit|1970|p=150}}</ref>

== Catatan ==
{{Reflist}}

== Referensi ==
* {{cite news|first1=H. | last1=Siebeck | year=1846 | title= Ueber periodische Kettenbrüche
 |journal= J. Reine Angew. Math. | volume=33 | pages=68–70 | url=http://www.digizeitschriften.de/dms/resolveppn/?PID=PPN243919689_0033}}
* {{cite news|first1=J. B. H. | last1=Heilermann | title=Ueber die Verwandlung von Reihen in Kettenbrüche
 |journal =J. Reine Angew. Math. | volume=33 | pages=174–188 | url=http://www.digizeitschriften.de/dms/img/?PID=PPN243919689_0033| year=1846}}
* {{cite news| first1=Arne | last1=Magnus | title=Continued fractions associated with the Padé Table
 |journal=Math. Z. | volume=78 | pages=361–374 | year=1962}}
* {{cite news | first1=Chen-Fan | last1=Chen |first2=Leang-San | last2=Shieh
 |title=Continued fraction inversion by Routh's Algorithm | journal = IEEE Trans. Circuit Theory
 | volume=16 | number=2 | pages=197–202 | doi=10.1109/TCT.1969.1082925 | year=1969}}
* {{cite news|first1=William B. | last1=Gragg | title=Matrix interpretations and applications of the continued fraction algorithm
 |journal= Rocky Mount. J. Math. | volume=4 | number=2 | doi=10.1216/RJM-1974-4-2-213 | page=213 |year=1974}}
* {{Cite book | last = Jones | first = William B. | last2 = Thron | first2 = W. J. | title = Continued Fractions: Analytic Theory and Applications. Encyclopedia of Mathematics and its Applications. | place= | publisher = Addison-Wesley Publishing Company | year = 1980 | location = Reading. Massachusetts | volume = 11 | edition = | isbn = 0-201-13510-8}}
* {{cite book |title = Continued Fractions | year = 1964 | last1 = Khinchin | first1 = A. Ya. | authorlink = Aleksandr Khinchin | origyear = Originally published in Russian, 1935 | publisher = [[University of Chicago Press]] | ISBN= 0-486-69630-8 }}
* {{citation | first1 = Calvin T. | last1 = Long | year = 1972 | title = Elementary Introduction to Number Theory | edition = 2nd | publisher = [[D. C. Heath and Company]] | location = Lexington | lccn = 77-171950 }}
* {{cite book | first=Oskar | last= Perron | authorlink=Oskar Perron | title =Die Lehre von den Kettenbrüchen | publisher=Chelsea Publishing Company | place=New York, NY | year= 1950}}
* {{citation | first1 = Anthony J. | last1 = Pettofrezzo | first2 = Donald R. | last2 = Byrkit | year = 1970 | title = Elements of Number Theory | publisher = [[Prentice Hall]] | location = Englewood Cliffs | lccn = 77-81766 }}
* {{cite book | title = Continued Fractions | last1 = Rockett | first1 = Andrew M. | last2 = Szüsz | first2 = Peter| year = 1992 | publisher = 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}}
* {{cite book|first1=A. |last1= Cuyt |first2= V. | last2= Brevik Petersen |first3= B. |last3= Verdonk
 |first4= H. |last4= Waadeland |first5 = W. B. |last5=Jones |title =Handbook of Continued fractions for Special functions
 |publisher= Springer Verlag |year=2008 |isbn=978-1-4020-6948-2}}
* {{cite news | last1=Rieger |first1=G. J. | title =A new approach to the real numbers (motivated by continued fractions)
 |journal= Abh. Braunschweig.Wiss. Ges. | volume= 33 |year=1982 |pages=205–217}}

== Pranala luar ==
* {{springer|title=Continued fraction|id=p/c025540}}
* [http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html An Introduction to the Continued Fraction]
* Linas Vepstas [http://www.linas.org/math/chap-gap/chap-gap.html Continued Fractions and Gaps] (2004) reviews chaotic structures in continued fractions.
* [http://www.cut-the-knot.org/blue/ContinuedFractions.shtml Continued Fractions on the Stern-Brocot Tree] at [[cut-the-knot]]
* [http://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraI-0400/kyth3.html The Antikythera Mechanism I: Gear ratios and continued fractions]
* [http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html Continued fraction calculator], WIMS.
* [https://web.archive.org/web/20030202011209/http://www.tweedledum.com/rwg/cfup.htm Continued Fraction Arithmetic] Gosper's first continued fractions paper, unpublished. Cached on the [[Internet Archive]]'s [[Internet Archive#Wayback Machine|Wayback Machine]]
* {{MathWorld |title=Continued Fraction |urlname=ContinuedFraction}}
* [http://demonstrations.wolfram.com/ContinuedFractions/ Continued Fractions] by [[Stephen Wolfram]] and [http://demonstrations.wolfram.com/ContinuedFractionApproximationsOfTheTangentFunction/ Continued Fraction Approximations of the Tangent Function] by Michael Trott, [[Wolfram Demonstrations Project]].
* {{OEIS el|1=A133593|2="Exact" continued fraction for Pi}}
* [http://go.helms-net.de/math/tetdocs/FracIterAltGeom.htm A view into "fractional interpolation" of a continued fraction {{math|{1; 1, 1, 1, ...}}} ]
* [http://www.ams.org/publicoutreach/feature-column/fcarc-irrational3 Best rational approximation through continued fractions]

{{Wiktionary}}

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[[Kategori:Analisis matematika]]