Pecahan berlanjut: Perbedaan antara revisi

Konten dihapus Konten ditambahkan
123569yuuift (bicara | kontrib)
Tidak ada ringkasan suntingan
Tag: Suntingan perangkat seluler Suntingan peramban seluler Suntingan seluler lanjutan
Dedhert.Jr (bicara | kontrib)
memperbaiki istilah matematika
 
(5 revisi perantara oleh 2 pengguna tidak ditampilkan)
Baris 1:
{|class="wikitable" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:50px" width="120"
!bgcolor=#e7dcc3 colspan=2|''Artikel ini dalam proses pengembangan atau penambahan''
|}
{{thumb|width=220
|content=<math>a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{ \ddots + \cfrac{1}{a_n} }}}</math>
}}
 
Dalam [[matematika]], '''pecahan berlanjut''' atau '''pecahan kontinu''' ({{Lang-en|Continued fraction}}) adalah sebuah [[ekspresi (matematika)|ekspresi]] yang didapat melalui proses [[iteratif]] mewakili bilangan sebagai jawaban dari [[bagian integerbilangan bulat]]<nowiki/>nya.<ref>{{cite web|url=http://www.britannica.com/EBchecked/topic/135043/continued-fraction|title=Continued fraction - mathematics|publisher=}}</ref> IntegerBilangan bulat <math>a_i</math> disebut [[koefisien]] dari pecahan berlanjut.<ref name="Pettofrezzo 1970 150">{{harvtxt|Pettofrezzo|Byrkit|1970|p=150}}</ref>
 
== Motivasi dan notasi ==
 
== Rumus dasar ==
 
== Menghitung representasi pecahan berlanjut ==
 
== Notasi ==
 
== Pecahan lanjutan hingga ==
 
== Dari timbal balik ==
 
== Pecahan dan konvergensi yang tak terbatas ==
 
== Semikonvergensi ==
 
== Pendekatan rasional terbaik ==
 
== Perbandingan ==
 
== Ekspansi pecahan lanjutan dari π ==
 
== Fraksi lanjutan digeneralisasi ==
 
== Ekspansi fraksi lanjutan lainnya ==
 
== Aplikasi ==
 
== Contoh bilangan rasional dan irasional ==
 
== Sejarah ==
 
== Catatan ==
Baris 53 ⟶ 24:
|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 |url = https://archive.org/details/continuedfractio00khin_0 | 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 | url = https://archive.org/details/continuedfractio0000rock | 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