Results 11 to 20 of about 5,130,669 (296)
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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Axioms, 2023 The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are constructed.
T. Antonova +3 more
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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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On convergence of function F4(1,2;2,2;z1,z2) expansion into a branched continued fraction
Mathematical Modeling and Computing, 2022 In the paper, the possibility of the Appell hypergeometric function F4(1,2;2,2;z1,z2) approximation by a branched continued fraction of a special form is analysed.
V. Hladun +3 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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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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On the second Lyapunov exponent of some multidimensional continued fraction algorithms [PDF]
Mathematics of Computation, 2019 We study the strong convergence of certain multidimensional continued fraction algorithms. In particular, in the two-dimensional case, we prove that the second Lyapunov exponent of Selmer's algorithm is negative and bound it away from zero.
Val'erie Berth'e +2 more
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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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