Results 1 to 10 of about 19,232 (80)

Convergence criterion for branched contіnued fractions of the special form with positive elements

Karpatsʹkì Matematičnì Publìkacìï, 2017
In this paper the problem of convergence of the important type of a multidimensional generalization of continued fractions, the branched continued fractions with independent variables, is considered.
D.I. Bodnar, I.B. Bilanyk
doaj   +1 more source

The Convergence and Divergence of $q$-Continued Fractions outside the Unit Circle

Rocky Mountain Journal of Mathematics, 2006
9 pages.
Bowman, Douglas, McLaughlin, James
openaire   +4 more sources

Conical limit sets and continued fractions [PDF]

, 2007
Inspired by questions of convergence in continued fraction theory, Erdős, Piranian and Thron studied the possible sets of divergence for arbitrary sequences of Möbius maps acting on the Riemann sphere, S2.
Crane, Edward, Short, Ian
core   +3 more sources

On convergence of generalized continued fractions and Ramanujan's conjecture [PDF]

, 2004
We consider continued fractions \frac{-a_1}{1-\frac{a_2}{1-\frac{a_3}{1-...}}} \label{fr} with real coefficients $a_i$ converging to a limit $a$. S.Ramanujan had stated the theorem (see [ABJL], p.38) saying that if $a\neq\frac14$, then the fraction ...
Glutsyuk, A. A.
core   +3 more sources

Metrical Diophantine approximation for quaternions [PDF]

, 2014
Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup' sets.Comment: 30 pages.
Beresnevich, Beresnevich, Beresnevich, Beresnevich, BRENT EVERITT, Cassels, Conway, Dani, Dani, Dickinson, Dodson, Dodson, Dodson, Falconer, Federer, Hardy, Hardy, Harman, Harman, Jarník, Jarník, Koksma, MAURICE DODSON, Nicholls, Rogers, Schmidt, Speiser, Sprindžuk   +27 more
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Dynamics of a continued fraction of Ramanujan with random coefficients

Abstract and Applied Analysis, 2005
We study a generalization of a continued fraction of Ramanujan with random, complex-valued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of ...
Jonathan M. Borwein, D. Russell Luke
doaj   +1 more source

Quasi-normal modes of AdS black holes : A superpotential approach [PDF]

, 2000
A novel method, based on superpotentials is proposed for obtaining the quasi-normal modes of anti-de Sitter black holes. This is inspired by the case of the three-dimensional BTZ black hole, where the quasi-normal modes can be obtained exactly and are ...
Blome H-J, Chandrasekhar S, Danielsson U H, Kokkotas K D, Leaver E W, Nollert H, T R Govindarajan, V Suneeta, Vishveshvara C V, Witten E, Witten E   +10 more
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The Environmental Dependence of the Evolving S0 Fraction [PDF]

, 2010
We reinvestigate the dramatic rise in the S0 fraction, f_S0, within clusters since z ~ 0.5. In particular, we focus on the role of the global galaxy environment on f_S0 by compiling, either from our own observations or the literature, robust line-of ...
Andreon, Balogh, Balogh, Bekki, Christlein, Couch, Couch, David J. Sand, Dennis W. Just, Dennis Zaritsky, Desai, Dressler, Fasano, Finn, Gregory Rudnick, Hinz, Icke, Kannappan, Kautsch, Kendall, Mihos, Moore, Moran, Papovich, Poggianti, Poggianti, Poggianti, Postman, Sandage, Smail, Smith, Tran, Vandana Desai, Wechsler, Wilman, Yang, Yang, Zabludoff, Zabludoff   +38 more
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Derivation of Closed-Form Expressions in Apéry-like Series Using Fractional Calculus and Applications

Fractal and Fractional
This paper explores the Apéry-like series and demonstrates the derivation of closed-form expressions using fractional calculus. We consider a variety of Apéry-like functions, which were categorized by their functional forms and coefficients by applying ...
Ampol Duangpan, Ratinan Boonklurb, Udomsak Rakwongwan, Phiraphat Sutthimat   +3 more
doaj   +1 more source

Numerical Evidence that the Perturbation Expansion for a Non-Hermitian $\mathcal{PT}$-Symmetric Hamiltonian is Stieltjes

, 2000
Recently, several studies of non-Hermitian Hamiltonians having $\mathcal{PT}$ symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians.
Andrianov, Bagchi, Baker, Bender, Bender, Bender, Bender, Bender, Bender, Bender, Bender, Bender, Bender, Bender, Bender, Bender, Brezinski, Brezinski, Cannata, Carl M. Bender, Chishtie, Chishtie, Chishtie, Chishtie, Delabaere, Delabaere, Dorey, Elias, Ellis, Ellis, Ellis, Ernst Joachim Weniger, Graffi, Graves-Morris, Herbst, Hurst, Jack, Jentschura, Jentschura, Jones, Pham, Samuel, Samuel, Samuel, Samuel, Samuel, Samuel, Simon, Steele, Steinfelds, Thirring, Weniger, Weniger, Weniger, Weniger, Weniger, Weniger, Wu, Wynn, Znojil   +59 more
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