Results 191 to 200 of about 668 (225)

On some generalizations of Ramanujan’s continued fraction identities

Proceedings of the Indian Academy of Sciences - Section A, 1987
Many of the continued fraction expansions of Ramanujan can be viewed as special cases of the expansion of the ratio of basic hypergeometric series: \(_ 2\phi_ 1(a,b;c;xq)/_ 2\phi_ 1(a,b;c;x).\) The authors find the related expansions for the ratios in which the numerator has been replaced by one of a number of similar basic hypergeometric series.
D D Somashekara
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Generalization of continued fractions. I

Journal of Mathematical Sciences, 2012
We constructed a new algebraic object, namely, recursion fractions of the n th order that are n -dimensional generalizations of continued fractions. For the representation and the study of such fractions, we used paradeterminants and triangular matrices.
D. I. Bodnar, R. A. Zators’kyi
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Generalized continued fractions

Applied Mathematics and Computation, 2000
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The Khintchine constants for generalized continued fractions

Applied Mathematics and Computation, 2003
The authors study the limiting behaviour of the Khintchine constants for generalized continued fractions by computer simulations.
Geon Ho Choe, Chihurn Kim
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Convergence acceleration for generalized continued fractions

Transactions of the American Mathematical Society, 1988
The main result in this paper is the proof of convergence acceleration for a suitable modification (as defined by de Bruin and Jacobsen) in the case of an n n
Levrie, Paul, Jacobsen, Lisa
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Generalized continued fractions

Discrete Mathematics and Applications, 1998
The author considers a generalized continued fraction whose expression has the form \[ a_0+\frac{(-1)^{u_1}}{a_1+{\displaystyle \frac{(-1)^{u_2}}{a_2+{\displaystyle \frac{(-1)^{u_3}}{a_3+\dots}}}}}, \] where \(a_i\in\mathbb R\) (\(i=0,1,2,\dots\)) and \(u_i\in\{0,1\}\) (\(i=1,2,\dots\)). In this paper the concept how to represent a real number \(\alpha\
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Stable Evaluation of Generalized Continued Fractions

SIAM Journal on Numerical Analysis, 1981
An error analysis is given for the backward recurrence algorithm for generalized continued fractions. Bounds for the accumulated relative rounding error can be obtained by applying an extension of a technique by Jones and Thron [Math. Comp., 28 (1974), pp. 795–810].
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Generalized continued fractions and ergodic theory

Journal of Mathematical Sciences, 1999
A standard theory of one-dimensional continued fractions is based on the sequential application of the so-called Gauss map and the comparison of the result to zero. The author proposes a generalization of this procedure to the case when one uses some other map, say \(A\), and an arbitrary stopping rule (e.g., the comparison to a given value \(\omega ...
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Generalizing the continued fraction algorithm to arbitrary dimensions

30th Annual Symposium on Foundations of Computer Science, 1989
A new \(N\)-dimensional continued fraction algorithm is presented. Its most remarkable property is that it produces infinitely many solutions of the diophantine inequality \(\max_{1\leq i\leq N}| x_ i q-p_ i|\ll q^{-w(N)}\) with \(w(N)=1/2N(N+1)\). It also detects linear dependence.
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Convergence of generalized continued fractions

International Journal of Computer Mathematics, 1982
A general theory for the convergence of Generalized Continued Fractions, based on an inclusion property of complex regions, is given. Due to the appearance of divisions of complex regions, the theory cannot be applied in the general case. This is even so for the case of complex discs, but for these special regions the theory can be adjusted in order to
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