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Some convergence regions of branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 2013
Some circular and parabolic convergence regions for branched continued fractions of special form are established.
O.E. Baran
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On convergence criteria for branched continued fraction

Karpatsʹkì Matematičnì Publìkacìï, 2020
The starting point of the present paper is a result by E.A. Boltarovych (1989) on convergence regions, dealing with branched continued fraction \[\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^N\frac{a_{i(2)}}{1}{\atop+}\ldots{\atop+}\sum_{i_n=1}^N\
T.M. Antonova
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On the convergence of multidimensional S-fractions with independent variables

Karpatsʹkì Matematičnì Publìkacìï, 2020
The paper investigates the convergence problem of a special class of branched continued fractions, i.e. the multidimensional S-fractions with independent variables, consisting of \[\sum_{i_1=1}^N\frac{c_{i(1)}z_{i_1}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{c_{
O.S. Bodnar, R.I. Dmytryshyn, S.V. Sharyn   +2 more
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Truncation error bounds for branched continued fraction whose partial denominators are equal to unity

Математичні Студії, 2020
The paper deals with the problem of obtaining error bounds for branched continued fraction of the form $\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{a_{i(2)}}{1}{\atop+}\sum_{i_3=1}^{i_2}\frac{a_{i(3)}}{1}{\atop+}\ldots$.
R. I. Dmytryshyn, T. M. Antonova
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The scrambles of halton sequence and thier weaknesses [PDF]

Journal of Hyperstructures, 2020
So far, many scrambles have been introduced to break the correlation between Halton’s sequence points and improve itstwo-dimensional designs. In this paper, some of the most important scrambles that are available to scrambling the Halton sequence are ...
Behrouz Fathi Vajargah, Ali Mogharrabi Ostadkalayeh   +1 more
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Transcendental Continued Fractions

Communications in Mathematics, 2022
In the present paper, we give sufficient conditions on the elements of the continued fractions $A$ and $B$ that will assure us that the continued fraction $A^B$ is a transcendental number. With the same condition, we establish a transcendental measure of $A^B.$
Ahallal, Sarra, Kacha, Ali
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Continued fraction expansions for q-tangent and q-cotangent functions [PDF]

Discrete Mathematics & Theoretical Computer Science, 2010
For 3 different versions of q-tangent resp. q-cotangent functions, we compute the continued fraction expansion explicitly, by guessing the relative quantities and proving the recursive relation afterwards.
Helmut Prodinger
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Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$

Researches in Mathematics, 2022
Three- and four-term recurrence relations for hypergeometric functions of the second order (such as hypergeometric functions of Appell, Horn, etc.) are the starting point for constructing branched continued fraction expansions of the ratios of these ...
R.I. Dmytryshyn, I.-A.V. Lutsiv
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The Reciprocal of a Continued Fraction [PDF]

Proceedings of the American Mathematical Society, 1952
Stieltjes [3, Chapter X],1 and later Rogers [2], gave formulas by means of which the reciprocal continued fractions for continued fractions of a certain class may be determined. We give below a theorem which extends the class of continued fractions to which this reciprocal transformation is applicable ;2 moreover, the theorem is stated in terms of ...
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Polynomial continued fractions [PDF]

Acta Arithmetica, 2002
Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one.
Bowman, Douglas, McLaughlin, James
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