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- ...iří Horáček (physicist)|last2=Sasakawa|first2=T.|title=Method of continued fractions with application to atomic physics|journal=Physical Review A|volume=28|issu iteratively and to construct convergent [[continued fraction]] for the [[T-matrix]] ...6 KB (1,002 words) - 13:43, 1 February 2023
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- {{Short description|Criterion for convergence of continued fractions}} ...on be renamed the Śleszyński criterion?|journal=Comm. Anal. Theory Contin. Fractions|volume=1|year=1992|pages=13–20}}</ref> ...2 KB (289 words) - 12:20, 24 July 2023
- {{short description|On the rate of convergence of the continued fraction expansion of a typical real number}} ...theory]], '''Lochs's theorem''' concerns the rate of convergence of the [[continued fraction]] expansion of a typical real number. A proof of the theorem was p ...6 KB (889 words) - 19:49, 14 January 2024
- * [[continued fraction|infinite continued fractions]], such as ...ere the left hand side uses [[Carl Friedrich Gauss|Gauss]]'s [[generalized continued fraction|Kettenbruch notation]].<ref> ...3 KB (457 words) - 17:34, 10 June 2024
- ...e [[determinant]] of a [[tridiagonal matrix]] and having applications in [[continued fraction]]s. * Ratios of continuants represent (convergents to) [[continued fraction]]s as follows: ...5 KB (713 words) - 16:35, 11 November 2024
- Another way of expressing numbers is to write them as [[simple continued fraction]]s, as in: ...rational numbers require an infinite sequence to express them as continued fractions.<ref>{{citation|first=Leonhard|last=Euler|url=https://scholarlycommons.paci ...8 KB (1,152 words) - 03:54, 31 January 2025
- ...orithm''' is an [[algorithm]] to evaluate [[generalized continued fraction|continued fraction]]s, and was originally devised to compute tables of spherical [[Be ...Generating Bessel functions in Mie scattering calculations using continued fractions|url=http://dx.doi.org/10.1364/ao.15.000668|journal=Applied Optics|volume=15 ...9 KB (1,345 words) - 01:31, 12 February 2025
- ...iří Horáček (physicist)|last2=Sasakawa|first2=T.|title=Method of continued fractions with application to atomic physics|journal=Physical Review A|volume=28|issu iteratively and to construct convergent [[continued fraction]] for the [[T-matrix]] ...6 KB (1,002 words) - 13:43, 1 February 2023
- ...named after [[Felix Klein]], is used to generalize the concept of [[simple continued fraction]]s to higher dimensions. == Relation to continued fractions == ...14 KB (2,157 words) - 16:29, 11 November 2024
- ...ainst [[RSA (algorithm)|RSA]]. The attack uses [[simple continued fraction|continued fraction representation]] to expose the private key ''d'' when ''d'' is sma ...ons]] expansion of {{sfrac|''e''|''N''}}. Note that this algorithm finds [[fractions]] in their lowest terms. We know that ...12 KB (1,751 words) - 15:49, 21 February 2025
- ...(mathematician)|Narayana Pandita]] used the knowledge of simple recurring continued fraction in the solutions of indeterminate equations of the type <math>nx^2 Contains rules for writing a fraction as a sum of unit fractions. 22 rules and 14 examples.<ref name=mii27/> ...8 KB (1,168 words) - 08:14, 7 November 2024
- ...up="note>https://www.math.ucla.edu/~wdduke/preprints/bams4.pdf ''Continued Fractions and Modular Functions'', W. Duke, pp 22-23</ref> The function <math>\eta(\t ...rst1=William | author1-link=William Duke (mathematician) | title=Continued Fractions and Modular Functions | year=2005 | url=https://www.math.ucla.edu/~wdduke/p ...8 KB (1,270 words) - 13:41, 1 March 2023
- ...xander Ostrowski]], is either of two related numeration systems based on [[continued fraction]]s: a [[non-standard positional numeral system]] for integers and Fix a positive [[irrational number]] ''α'' with [[continued fraction]] expansion [''a''<sub>0</sub>; ''a''<sub>1</sub>, ''a''<sub>2</su ...3 KB (492 words) - 18:01, 12 March 2023
- ...link= Lisa Lorentzen |title=On the Bauer-Muir transformation for continued fractions and its applications|journal=Journal of Mathematical Analysis and Applicati ...tierung]] under [[Peter Gustav Lejeune Dirichlet]]. From 1842 Gustav Bauer continued his studies in [[Paris]] under [[Joseph Liouville]], as well as other mathe ...7 KB (995 words) - 20:28, 26 October 2024
- ...–470}}</ref><ref>{{cite book |last1=Khinchin |first1=A.I. |title=Continued Fractions |date=1964 |publisher=University of Chicago Press}}</ref> Baum and Sweet's ...237-248 |doi-access=free }}</ref> proved that the partial quotients of the continued fraction for <math>f</math> above do not form an automatic sequence.<ref>Al ...7 KB (989 words) - 03:39, 26 December 2024
- {{short description|Continued fraction closely related to the Rogers–Ramanujan identities}} The '''Rogers–Ramanujan continued fraction''' is a [[continued fraction]] discovered by {{harvtxt|Rogers|1894}} and independently by [[S ...29 KB (4,572 words) - 22:02, 24 April 2024
- ...f (123) patterns"<ref name=":1" /> with the result being "in the form of a continued fraction".<ref name=":1" /> Robertson's contribution to this specific paper ...7 KB (977 words) - 10:14, 27 April 2024
- ...ed [[Stern–Brocot tree]]. Even earlier, a similar tree (including only the fractions between 0 and 1) appears in [[Johannes Kepler|Kepler's]] ''[[Harmonices Mun ...level just below the top of the tree, reading from left to right, then the fractions on the next level down, reading from left to right, etc." {{harvtxt|Gibbons ...16 KB (2,279 words) - 09:18, 6 January 2025
- {{Short description|A mathematical conjecture involving continued fractions}} ...frach-Stav in 2023.<ref>Naccache, D., Yifrach-Stav, O. (2023). The Balkans Continued Fraction. arXiv preprint arXiv:2308.06291. Available at: [https://arxiv.org ...8 KB (1,222 words) - 13:51, 26 February 2025
- ...native formulations of [[Generalized continued fraction|analytic continued fractions]], [[series (mathematics)|series]], [[product (mathematics)|products]] and ...<sub>n</sub>∘⋯∘f<sub>1</sub>(z) in computing the fixed points of continued fractions, products, and series |journal=Appl. Numer. Math. |volume=8 |issue=6 |pages ...26 KB (4,221 words) - 09:10, 20 January 2025
- ...d fraction#Infinite continued fractions and convergents|convergents of the continued fraction]] are the best [[Diophantine approximation|approximations by ratio ...rüche (On the approximate representation of irrational numbers by rational fractions)|journal=[[Mathematische Annalen]]|language=de|url=https://gdz.sub.uni-goet ...12 KB (1,810 words) - 13:02, 22 January 2025