Results 11 to 20 of about 1,866,320 (298)
A Specialised Continued Fraction [PDF]
Canadian Journal of Mathematics, 1993 AbstractWe display a number with a surprising continued fraction expansion and show that we may explain that expansion as a specialisation of the continued fraction expansion of a formal series: A series ΣchX-h has a continued fraction expansion with partial quotients polynomials in X of positive degree (other, perhaps than the 0-th partial quotient ...
van der Poorten, A. J., Shallit, J.
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An unusual continued fraction [PDF]
Proceedings of the American Mathematical Society, 2015 We consider the real number σ \sigma ...
Badziahin, D., Shallit, J.
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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 fractions which correspond to two series expansions and the strong Hamburger moment problem [PDF]
, 2012 Just as the denominator polynomials of a J-fraction are orthogonal polynomials with respect to some moment functional, the denominator polynomials of an M-fraction are shown to satisfy a skew orthogonality relation with respect to a stronger moment ...
Sri Ranga, A.
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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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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 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 +1 more
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A Theorem on Continued Fractions [PDF]
Proceedings of the Edinburgh Mathematical Society, 1959 One of the outstanding theorems in the theory of continued fractions is the result described by O. Perron, Die Lehre von den Kettenbrüchen (1912, 1929, 1954–7) as the transformation of Bauer and Muir (for brevity I shall call it the BM theorem); this theorem and limiting cases of it give rise to numerous extremely interesting consequences.
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A CONTINUED FRACTION TITBIT [PDF]
Fractals, 1995 In 1812 Gauss, in a letter to Laplace, proposed without proof a formula explaining the statistical regularity of continued fractions. There has since been speculation concerning the manner in which Gauss arrived at this formula. In this article we present a plausible explanation, which at the same time gives an elementary proof of the full ergodic ...
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