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Longer titles found: Continued fraction expansion (view), Continued fraction factorization (view), Simple continued fraction (view), Euler's continued fraction formula (view), Periodic continued fraction (view), Gauss's continued fraction (view), Solving quadratic equations with continued fractions (view), Rogers–Ramanujan continued fraction (view), Method of continued fractions (view)

searching for Continued fraction 59 found (330 total)

alternate case: continued fraction

Catalan's constant (3,484 words) [view diff] exact match in snippet view article find links to article

{5^{4}}{24+{\cfrac {7^{4}}{32+{\cfrac {9^{4}}{40+\ddots }}}}}}}}}}}}} The simple continued fraction is given by: G = 1 1 + 1 10 + 1 1 + 1 8 + 1 1 + 1 88 + ⋱ {\displaystyle

Ornstein isomorphism theorem (675 words) [view diff] exact match in snippet view article find links to article

Sinai's billiards, ergodic automorphisms of the n-torus, and the continued fraction transform. The theorem is actually a collection of related theorems

Little q-Laguerre polynomials (387 words) [view diff] exact match in snippet view article find links to article

orthogonal polynomials in the basic Askey scheme closely related to a continued fraction studied by Wall (1941). (The term "Wall polynomial" is also used for

Hypergeometric function (7,168 words) [view diff] exact match in snippet view article find links to article

several ways to write a quotient of two hypergeometric functions as a continued fraction, for example: 2 F 1 ( a + 1 , b ; c + 1 ; z ) 2 F 1 ( a , b ; c ;

Lentz's algorithm (1,170 words) [view diff] exact match in snippet view article find links to article

functions of complex arguments can be difficult. He developed a new continued fraction technique for calculating the ratios of spherical Bessel functions

Richard Schroeppel (458 words) [view diff] exact match in snippet view article find links to article

While not entirely rigorous, his proof that Morrison and Brillhart's continued fraction factoring algorithm ran in roughly e 2 ln ⁡ n ln ⁡ ln ⁡ n {\displaystyle

Jackson q-Bessel function (2,730 words) [view diff] exact match in snippet view article find links to article

Olshanetsky & Rogov (1995). The ratio of modified q-Bessel functions form a continued fraction (Ismail (1981)): I ν ( 2 ) ( z ; q ) I ν − 1 ( 2 ) ( z ; q ) = 1 2

Ionica Smeets (487 words) [view diff] case mismatch in snippet view article find links to article

Volkskrant). She completed her PhD at Leiden in 2010; her dissertation, On Continued Fraction Algorithms, was supervised by Robert Tijdeman and Cornelis Kraaikamp

List of topics related to π (159 words) [view diff] exact match in snippet view article find links to article

involving π Liu Hui's π algorithm Mathematical constant (sorted by continued fraction representation) Mathematical constants and functions Method of exhaustion

P Kesava Menon (385 words) [view diff] exact match in snippet view article find links to article

classical inequality theorem" He published a paper on the subject of the continued fraction of the mathematician Ramanujan, as noted here in the Journal of the

C99 (2,608 words) [view diff] exact match in snippet view article find links to article

(annex F). The following annotated example C99 code for computing a continued fraction function demonstrates the main features: #include <stdio.h> #include

Complex plane (4,502 words) [view diff] exact match in snippet view article find links to article

necessary, and not just convenient. Consider the infinite periodic continued fraction f ( z ) = 1 + z 1 + z 1 + z 1 + z ⋱ . {\displaystyle f(z)=1+{\cfrac

K. G. Ramanathan (599 words) [view diff] exact match in snippet view article find links to article

National Science Academy Honorary fellow of TIFR. On Ramanujan’s continued fraction, KG Ramanathan - Acta Arith, 1984 Some applications of Kronecker’s

Herman ring (1,183 words) [view diff] exact match in snippet view article find links to article

edge of the Mandelbrot set with irrational winding number having continued fraction expansion with bounded denominators. The irrational numbers are of

29 (number) (1,134 words) [view diff] exact match in snippet view article

2016-05-31. "Sloane's A086383 : Primes found among the denominators of the continued fraction rational approximations to sqrt(2)". The On-Line Encyclopedia of Integer

Al-Salam–Ismail polynomials (66 words) [view diff] exact match in snippet view article find links to article

(1983), "Orthogonal polynomials associated with the Rogers–Ramanujan continued fraction", Pacific Journal of Mathematics, 104 (2): 269–283, doi:10.2140/pjm

Baum–Sweet sequence (994 words) [view diff] exact match in snippet view article find links to article

non-quadratic algebraic real number having bounded partial quotients in its continued fraction expansion. A counterexample to this conjecture is still not known

Electronic filter (1,599 words) [view diff] no match in snippet view article find links to article

the filter. The actual element values of the filter are obtained by continued-fraction or partial-fraction expansions of this polynomial. Unlike the image

Lattice delay network (7,145 words) [view diff] exact match in snippet view article find links to article

are not possible, so some form of approximation has to be used. A continued fraction expansion of tanh(x) is tanh ⁡ ( x ) = 1 1 x + 1 3 x + 1 5 x + 1 7

Approximation error (1,153 words) [view diff] exact match in snippet view article find links to article

1/√2 (red octagon) and 1/√3 (orange triangle) calculated from their continued fraction expansions, plotted as slopes y/x with errors from their true values

George Szekeres (636 words) [view diff] exact match in snippet view article find links to article

portal Mathematics portal Powerful number Szekeres snark Generalized continued fraction Kruskal–Szekeres coordinates Szekeres–Wilf number Schröder's equation

Derrick Norman Lehmer (537 words) [view diff] exact match in snippet view article find links to article

PMID 16576302. Lehmer, D. N. (1918). "On Jacobi's extension of the continued fraction algorithm". Proc Natl Acad Sci U S A. 4 (12): 360–364. Bibcode:1918PNAS

List of knot theory topics (788 words) [view diff] exact match in snippet view article find links to article

Dowker–Thistlethwaite notation (DT notation) Gauss code (see also Gauss diagrams) continued fraction regular form 2-bridge knot Alternating knot; a knot that can be represented

Cube root (1,968 words) [view diff] exact match in snippet view article find links to article

approximation by dividing the exponent by 3. Also useful is this generalized continued fraction, based on the nth root method: If x is a good first approximation

Johann Heinrich Lambert (2,280 words) [view diff] exact match in snippet view article find links to article

credited with the first proof that π is irrational using a generalized continued fraction for the function tan x. Euler believed the conjecture but could not

Tangle (mathematics) (987 words) [view diff] exact match in snippet view article

(a_{0},a_{1},a_{2},\dots )} is then defined as the number given by the continued fraction [ a n , a n − 1 , a n − 2 , … ] {\displaystyle [a_{n},a_{n-1},a_{n-2}

Peter Wynn (mathematician) (1,540 words) [view diff] exact match in snippet view article

S2CID 120390887. Wynn, Peter (1963). "Note on a converging factor for a certain continued fraction". Numerische Mathematik. 5 (1): 332–352. doi:10.1007/BF01385901. S2CID 118433217

List of numbers (3,931 words) [view diff] exact match in snippet view article find links to article

Nishioka and Iekata Shiokawa; 'Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers'; "A001620 - OEIS". oeis

Peter Orno (1,659 words) [view diff] no match in snippet view article find links to article

another peer-reviewed journal of the MAA: Quet, L.; Ørno, P. (2006). "A continued fraction related to π (Problem 11102, 2004, p. 626)". American Mathematical

James Alexander Shohat (597 words) [view diff] exact match in snippet view article find links to article

Sherman: Shohat, J.; Sherman, J. (1932). "On the numerators of the continued fraction". Proc Natl Acad Sci U S A. 18 (3): 283–287. doi:10.1073/pnas.18.3

Madhava of Sangamagrama (3,711 words) [view diff] exact match in snippet view article find links to article

correction terms. They are the first three convergents of a finite continued fraction, which, when combined with the original Madhava's series evaluated

Exponential integral (2,995 words) [view diff] exact match in snippet view article find links to article

{x}}_{k}&\triangleq [x^{0},x^{1},\dots ,x^{k}]^{T}\end{aligned}}} The continued fraction expansion E 1 ( x ) = e − x x + 1 1 + 1 x + 2 1 + 2 x + 3 ⋱ . {\displaystyle

Vera W. de Spinadel (2,276 words) [view diff] case mismatch in snippet view article find links to article

2000 "Half-regular Continued Fraction Expansions and Design", Journal of Mathematics & Design 1 ( 1) marzo 2001 "Continued Fraction Expansions and Design"

Evan O'Dorney (747 words) [view diff] exact match in snippet view article find links to article

$100,000, in the Intel Science Talent Search for a project entitled "continued fraction convergents and linear fractional transformations". O'Dorney started

Knot theory (6,295 words) [view diff] exact match in snippet view article find links to article

1-vertex basic polyhedron. The 2 −3 2 is a sequence describing the continued fraction associated to a rational tangle. One inserts this tangle at the vertex

Digital filter (3,638 words) [view diff] exact match in snippet view article find links to article

order subsections Parallel lower (typical second) order subsections Continued fraction expansion Lattice and ladder One, two and three-multiply lattice forms

Nonstandard calculus (3,979 words) [view diff] exact match in snippet view article find links to article

that the Dirichlet function is not continuous at π. Consider the continued fraction approximation an of π. Now let the index n be an infinite hypernatural

Cantor function (3,390 words) [view diff] exact match in snippet view article find links to article

out" form of the latter; it can be constructed by passing from a continued fraction expansion to a binary expansion, just as the Cantor function can be

Aaron Robertson (mathematician) (748 words) [view diff] exact match in snippet view article

number of (123) patterns" with the result being "in the form of a continued fraction". Robertson's contribution to this specific paper includes discussion

Samarendra Nath Biswas (456 words) [view diff] exact match in snippet view article find links to article

supersymmetric quantum mechanics, stochastic quantization, quark stars, continued fraction theory, role of parastatistics in statistical mechanics, Biswas has

Omar Khayyam (9,193 words) [view diff] exact match in snippet view article find links to article

equal ratios, he redefined the concept of a number by the use of a continued fraction as the means of expressing a ratio. Youschkevitch and Rosenfeld argue

Riemann zeta function (10,583 words) [view diff] no match in snippet view article find links to article

1016/S0377-0427(02)00358-8. MR 1906742. Cvijović, Djurdje; Klinowski, Jacek (1997). "Continued-fraction expansions for the Riemann zeta function and polylogarithms". Proc

Fresnel integral (2,715 words) [view diff] exact match in snippet view article find links to article

argument. For large argument, asymptotic expansions converge faster. Continued fraction methods may also be used. For computation to particular target precision

Jiří Čížek (931 words) [view diff] case mismatch in snippet view article find links to article

Vrscay, E.R. (1982). "Asymptotic Estimation of the Coefficients of the Continued Fraction ˇ Representing the Binet Function". C.R. Math. Rep. Acad. Sci. Canada

S. C. Dutta Roy (2,597 words) [view diff] exact match in snippet view article find links to article

"Rational approximation of some irrational functions through a flexible continued fraction expansion". Proceedings of the IEEE. 70 (1): 84–85. doi:10.1109/PROC

Floating-point arithmetic (14,095 words) [view diff] exact match in snippet view article find links to article

final R t o t {\displaystyle R_{tot}} of 0, as expected (see the continued fraction example of IEEE 754 design rationale for another example). Overflow

Numerical semigroup (1,417 words) [view diff] exact match in snippet view article find links to article

be the unique integer such that a2s0 ≡ a3 mod a1, 0 ≤ s0 < a1. The continued fraction algorithm is applied to the ratio a1/s0: a1 = q1s0 − s1, 0 ≤ s1 <

List of BASIC dialects (7,254 words) [view diff] exact match in snippet view article find links to article

prime test, factorization algorithms (Pollard rho, elliptic curve, continued fraction, quadratic sieve), etc. ASIC (DOS on the PC) Assembler PICAXE chip

Marjorie Devaney (756 words) [view diff] case mismatch in snippet view article find links to article

10 (1972): 130–36. Richtmyer, R., Devaney, M., and Metropolis, N. "Continued Fraction Expansions of Algebraic Numbers." Numerische Mathematik 4, no. 1 (1962):

Polylogarithm (10,165 words) [view diff] no match in snippet view article find links to article

1093/qmath/os-6.1.13. JFM 61.0395.02. Cvijovic, D.; Klinowski, J. (1997). "Continued-fraction expansions for the Riemann zeta function and polylogarithms" (PDF)

Analogue filter (9,034 words) [view diff] exact match in snippet view article find links to article

found ladder realisations of the network using Thomas Stieltjes' continued fraction expansion. This work was the basis on which network synthesis was

Computable topology (3,333 words) [view diff] exact match in snippet view article find links to article

\mathbb {R} } where the Böhm tree of a given set is similar to the continued fraction of a real number, and what is more, the Böhm tree corresponding to

Holomorphic Embedding Load-flow method (2,491 words) [view diff] exact match in snippet view article find links to article

states that the diagonal and supra-diagonal Padé (or equivalently, the continued fraction approximants to the power series) converge to the maximal analytic

Strähle construction (4,987 words) [view diff] exact match in snippet view article find links to article

{41}{29}}} for the half-octave, which is one of the convergents of the continued fraction expansion of the 2 {\displaystyle \scriptstyle {\sqrt {2}}} , and

Brahmagupta polynomials (1,373 words) [view diff] exact match in snippet view article find links to article

x_{n}=1,1,3,7,17,41,99,239,577,\ldots } which are the numerators of continued fraction convergents to 2 {\displaystyle {\sqrt {2}}} . This is also the sequence

Glossary of invariant theory (4,614 words) [view diff] exact match in snippet view article find links to article

degree 1 in the second. cumulant The numerator or denominator of a continued fraction, often expressed as a determinant. Sylvester (1853, Glossary p. 543–548)

Vladimir Pletser (4,296 words) [view diff] exact match in snippet view article find links to article

(1): 262–269. Retrieved 7 November 2023. Pletser, V. (2013). "On continued fraction development of quadratic irrationals having all periodic terms but

Lattice network (8,453 words) [view diff] exact match in snippet view article find links to article

3333p+p^{2}}}} The admittance Y1, where Y1 = 1/Z1 can be expressed as a continued fraction containing four terms, thus Y 1 ( p ) = p 2 + 10.333 p + 3.3333 20

Nome (mathematics) (13,956 words) [view diff] exact match in snippet view article

On the solution of the general quintic using the Rogers–Ramanujan continued fraction. Pella, Makedonien, Griechenland, 2015 Nikolaos Bagis: Solution of