Results 251 to 260 of about 1,656,816 (274)

On Koch's convergence criterion for branching continued fractions

Journal of Soviet Mathematics, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

On the Convergence of Branched Continued Fractions of a Special form in Angular Domains

Journal of Mathematical Sciences, 2020
We study the angular domains of convergence of branched continued fractions of a special form with complex partial denominators. By using the sufficient criterion of convergence of these fractions with positive elements and the Stieltjes–Vitali theorem, we establish a many-dimensional analog of the van Vleck convergence criterion for continued ...
D. I. Bodnar, I. B. Bilanyk
openaire   +1 more source

Some twin regions of convergence for branched continued fractions

Journal of Mathematical Sciences, 1998
See the review in Zbl 0891.40006.
openaire   +2 more sources

Representation of algebraic numbers by periodic branching continued fractions

Moscow University Mathematics Bulletin, 2007
The notion of a periodic branching continued fraction is a natural generalization of the notion of a periodic continued fraction. It is shown that for an arbitrary positive algebraic number one can construct a periodic branching continued fraction with natural elements convergent to this number.
openaire   +1 more source

Pringsheim-type convergence indicators for branching continued fractions

Ukrainian Mathematical Journal, 1989
A convergence test of Pringsheim type for the branching continued fraction (*) \(^{\infty}_{k=1}\sum^{N}_{i(k)=1}\frac{a(i(k))}{b(i(k))}\) with complex number elements is derived. It is shown that if \(| b(i(k))| \geq N | a(i(k))| +1\) for all corresponding partial denominators and numerators b(i(k)) and a(i(k)) occurring in (*), then this expansion ...
openaire   +2 more sources

Convergence criteria for branched continued fractions with nonnegative components

Journal of Mathematical Sciences, 1998
The paper addresses branched continued fractions with nonnegative components and a fixed or variable number of branchings. The author establishes necessary and sufficient conditions for their approximants to be well defined. The known Seidel-Stern and Stern convergence criteria for continued fractions are extended to continued fractions with positive ...
openaire   +2 more sources

Approximation of the lauricella hypergeometric functionsF D (N) by branched continued fractions

Journal of Mathematical Sciences, 1998
See the review in Zbl 0893.33008.
openaire   +2 more sources

Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H3 Ratios

Mathematics, 2021
Tamara Antonova, Viktoriia Kravtsiv, Roman Dmytryshyn   +2 more
exaly  

Generalized Hypergeometric Function 3F2 Ratios and Branched Continued Fraction Expansions

Axioms, 2021
Tamara Antonova, Serhii Sharyn, Roman Dmytryshyn   +2 more
exaly  

On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios

Axioms, 2023
Tamara Antonova, Serhii Sharyn, Roman Dmytryshyn   +2 more
exaly