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A continued fraction of order twelve
Open Mathematics, 2008 In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan's continued fraction and Ramanujan's cubic continued fraction. ©
Mahadeva Naika M. +2 more
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On generalization of continued fraction of Gauss [PDF]
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
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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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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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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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