Results 21 to 30 of about 291,339 (267)

Convergence criteria of branched continued fractions

Researches in Mathematics
The convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed.
I.B. Bilanyk, D.I. Bodnar, O.G. Vozniak
doaj   +1 more source

On generalization of continued fraction of Gauss

International Journal of Mathematics and Mathematical Sciences, 1990
In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2's which generalize Gauss' continued fraction for the ratio of two 2F1's.
Remy Y. Denis
doaj   +1 more source

Some properties of branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 2015
The fact that the values of the approximates of the positive definite branched continued fraction of special form are all in a certain circle is established for the certain conditions.
R.I. Dmytryshyn
doaj   +1 more source

Representation of Some Ratios of Horn’s Hypergeometric Functions H₇ by Continued Fractions

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7 ...
Tamara Antonova, Roman Dmytryshyn, Pavlo Kril, Serhii Sharyn   +3 more
doaj   +1 more source

Tasoev's continued fractions and Rogers–Ramanujan continued fractions

Journal of Number Theory, 2004
The author of this paper discusses Tasoev's continued fractions, which are of the form \[ [0;\underbrace{a,\dots,a}_m,\underbrace{a^2,\dots,a^2}_m, \dots]\equiv[0;\underbrace{\overline{a^k,\dots,a^k}}_m]_{k=1}^\infty,\;(m\geq1), \] and for a modified form he proves that \[ [0;\overline{ua^{2k-1}-1,1,va^{2k}-1}]_{k=1}^\infty=\frac{\sum_{s=0}^\infty u ...
openaire   +1 more source

Parametric Evaluations of the Rogers-Ramanujan Continued Fraction

International Journal of Mathematics and Mathematical Sciences, 2011
In this paper with the help of the inverse function of the singular moduli we evaluate the Rogers-Ranmanujan continued fraction and its first derivative.
Nikos Bagis
doaj   +1 more source

Generalized Hypergeometric Function ₃F₂ Ratios and Branched Continued Fraction Expansions

Axioms, 2021
The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensional ...
Tamara Antonova, Roman Dmytryshyn, Serhii Sharyn   +2 more
doaj   +1 more source

Continued Fractions and Linear Fractional Transformations

Integers, 2014
Rational approximations to a square root $\sqrt{k}$ can be produced by iterating the transformation $f(x) = (dx+k)/(x+d)$ starting from $\infty$ for any positive integer $d$. We show that these approximations coincide infinitely often with continued fraction convergents if and only if $4d^2/(k-d^2)$ is an integer, in which case the continued fraction ...
openaire   +5 more sources

Approximation by continued fractions [PDF]

Proceedings of the American Mathematical Society, 1974
Let x x be a real irrational number whose continued fraction has infinitely many partial quotients not less than
openaire   +1 more source

Stability to perturbations of continued fraction approximants and applications

Researches in Mathematics
The paper investigates the problem of stability to perturbations of continued fraction approximants with complex elements. Unlike the problem of investigating the stability of continued fractions to perturbations, which focuses on the properties of ...
V. Hladun, M. Dmytryshyn
doaj   +1 more source