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A note on the length of some finite continued fractions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, based on a 2008 result of Lasjaunias, we compute the lengths of simple continued fractions for some rational numbers whose numerators and denominators are explicitly given.
Khalil Ayadi, Chiheb Ben Bechir
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Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H3 Ratios
Mathematics, 2021 The paper deals with the problem of construction and investigation of branched continued fraction expansions of special functions of several variables. We give some recurrence relations of Horn hypergeometric functions H3. By these relations the branched
Tamara Antonova +2 more
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Parabolic convergence regions of branched continued fractions of the special form
Karpatsʹkì Matematičnì Publìkacìï, 2021 Using the criterion of convergence of branched continued fractions of the special form with positive elements, effective sufficient criteria of convergence for these fractions are established.
D.I. Bodnar, I.B. Bilanyk
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Karpatsʹkì Matematičnì Publìkacìï, 2021 The paper deals with the problem of approximation of functions of several variables by branched continued fractions. We study the correspondence between formal multiple power series and the so-called "multidimensional $S$-fraction with independent ...
R.I. Dmytryshyn, S.V. Sharyn
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Continued Fractions of Higher Order Polygonal Numbers with Respect to Order and Rank [PDF]
E3S Web of Conferences, 2023 Developing number sequence based on polygonal numbers is an enthusiastic field in number theory. As tetrahedral numbers are similar to pyramids, one of the Seven wonders of the World, yields a unique copiousness in its suitability. In number theory study
Anitha B., Balamurugan P.
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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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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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International Journal of Number Theory, 2006 We use the method of generating functions to find the limit of a q-continued fraction, with 4 parameters, as a ratio of certain q-series. We then use this result to give new proofs of several known continued fraction identities, including Ramanujan's continued fraction expansions for (q2; q3)∞/(q; q3)∞and [Formula: see text]. In addition, we give a new
Bowman, Douglas +2 more
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Continued Fraction Interpolation of Preserving Horizontal Asymptote
Journal of Mathematics, 2022 The classical Thiele-type continued fraction interpolation is an important method of rational interpolation. However, the rational interpolation based on the classical Thiele-type continued fractions cannot maintain the horizontal asymptote when the ...
Yushan Zhao, Kaiwen Wu, Jieqing Tan
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An unusual continued fraction [PDF]
Proceedings of the American Mathematical Society, 2015 We consider the real number $σ$ with continued fraction expansion $[a_0, a_1, a_2,\ldots] = [1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,\ldots]$, where $a_i$ is the largest power of $2$ dividing $i+1$. We compute the irrationality measure of $σ^2$ and demonstrate that $σ^2$ (and $σ$) are both transcendental numbers. We also show that certain partial quotients of
Badziahin, D., Shallit, J.
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