Continued Fraction
The random continued fraction transformation
... random continued fraction map ...convergent continued fraction expansions for all points in its domain and we explore some of the properties of these ...
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Design of Fractional order Recursive Digital Differentiator using Continued Fraction Expansion
... Abstract- In this paper, new discretized models of fractional order differentiator (FOD) based on different operators are proposed. Specifically in this work, one-third and one-fourth order differentiator models based on ...
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Invariant measures for continued fraction algorithms with finitely many digits
... In Section 2 we will give the general form of the continued fraction maps we study in this paper. After that we give several examples of such maps and a way of finding the density of the invariant measure ...
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On the real quadratic fields with certain continued fraction expansions and fundamental units
... pq) and investigated unit group of such real quadratic field. Also, they proved class number of quartic field using Sinnott’s index formula. Mollin and Williams determined positive square free integers d with class ...
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An Efficient Continued Fraction Algorithm for Nonlinear Optimization and Its Computer Implementation
... In this paper, we present an iterative algorithm for the problem based on the continued fraction interpolation method. For the general iteration scheme of n points, the algorithm constructs the n + 1th ...
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Continued Fraction Evaluation of Jn (X)/Jn-1 (X)
... evaluate continued fraction from the top down and was applied very successfully for the initial value problem[Sharaf and Sharaf ...the continued fraction is written ...
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Some new continued fraction sequence convergent to the Somos quadratic recurrence constant
... Remark It is worth to point out that Lemma provides some continued fraction in- equalities by the multiple-correction method. Similarly, repeating the above approach step by step, we can get more sharp ...
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Continued Fraction Method for Approximation of Heat Conduction Dynamics in a Semi Infinite Slab
... Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler com- putations and analyses. ...
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Elementary Proof of Yu V Nesterenko Expansion of the Number Zeta(3) in Continued Fraction
... Applications of difference equations to the Number Theory have a long history. For example, one can find in this journal several articles connected with the mentioned applications see 1–8. The interest in this area ...
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Algorithm for Fast Calculation of Hirzebruch Jung Continued Fraction Expansions to Coding of Graph Manifolds
... HJ-continued fraction expansion to solve the problems of the coupling constant hierarchy [5] [12] [13] and fine tuning [14] on the base of Kaluza-Klein approach in the multidimensional topological field ...
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Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets : a hundred decimal digits for the dimension of E2
... allowed continued fraction digits, an appropriate disc which is contracted by these mappings, and an associated transfer operator acting on the Hilbert Hardy space of analytic functions on this ...
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Generalization for character formulas in terms of continued fraction identities
... on continued fraction identities and recent results on character formulas for mock theta functions of Ramanujan given by Folsom [2], those are useful to the rest of the ...
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Continued Fraction Evaluation of the Universal Y’s Functions
... of continued fraction. Traditionally, either the fraction was computed from the bottom up, or the numerator and denominator of the nth convergent were accumulated separately with three-term ...
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A Wirsing type approach to some continued fraction expansion
... other continued fraction expansions: the continued fraction expansion to the nearest integer, grotesque expansion, Nakada’s α-expansions, Rosen expansions; in fact, there are too many to ...
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Modular Identities and Explicit Evaluations of a Continued Fraction of Ramanujan
... Ramanujan recorded many q-continued fractions and some of their explicit values in his second notebook 1 and in his lost notebook 2. The following beautiful continued fraction identity was recorded ...
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18.On modular equations and Lambert series for a continued fraction of Ramanujan
... In section 4, we prove a generalized Lambert series and write number of generalized Lambert series for theseG1(q) and H1(q) and for the continued fraction C(q)... Recall the following tw[r] ...
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Parametric Evaluations of the Rogers Ramanujan Continued Fraction
... Research Article Parametric Evaluations of the Rogers-Ramanujan Continued Fraction Nikos Bagis Department of Informatics, Aristotle University of Thessaloniki, Thessaloniki, Greece Corre[r] ...
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Continued fraction inequalities for the Euler Mascheroni constant
... Mortici, C: Optimizing the rate of convergence in some new classes of sequences convergent to Euler’s constant.. Mortici, C: A quicker convergence toward the gamma constant with the loga[r] ...
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A Gauss Kuzmin Lévy theorem for a certain continued fraction
... [24] T. A. Schmidt, Remarks on the Rosen λ-continued fractions, Number Theory with an Em- phasis on the Markoff Spectrum (Provo, Utah, 1991) (A. D. Pollington and W. Moran, eds.), Lecture Notes in Pure and Appl. ...
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Some sharp continued fraction inequalities for the Euler Mascheroni constant
... In this paper, starting from the sequence νn, based one the works of Mortici, Chen and Lu, we provide some new classes of convergent sequences with faster rate of convergence for the Eul[r] ...
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