Results 11 to 20 of about 1,237,080 (283)
Smarandache Continued Fractions [PDF]
, 2001 The theory of general continued fractions is developed to the extent required in order to calculate Smarandache continued fractions to a given number of decimal places. Proof is given for the fact that Smarandache general continued fractions built with positive integer Smarandache sequences baving only a finite number of terms equal to 1 is convergent.
Ibstedt, H.
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Tasoev's continued fractions and Rogers–Ramanujan continued fractions [PDF]
Journal of Number Theory, 2004 The author of this paper discusses Tasoev's continued fractions, which are of the form \[ [0;\underbrace{a,\dots,a}_m,\underbrace{a^2,\dots,a^2}_m, \dots]\equiv[0;\underbrace{\overline{a^k,\dots,a^k}}_m]_{k=1}^\infty,\;(m\geq1), \] and for a modified form he proves that \[ [0;\overline{ua^{2k-1}-1,1,va^{2k}-1}]_{k=1}^\infty=\frac{\sum_{s=0}^\infty u ...
Komatsu, Takao
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Some identities of G-continued fractions and generalized continued fractions [PDF]
Journal of Computational and Applied Mathematics, 1994 Generalized continued fractions and \(G\)-continued fractions are two different types of generalizations of continued fractions, the first one due to M. G. de Bruin, the second one introduced by P. Levrie and R. Piessens. Both types are related to higher order linear recurrence relations (whereas the ordinary ones are related to second order relations).
Levrie, Paul
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Some properties of continued fractions with applications in morkov processes [PDF]
, 1972 Several results for continued fractions are first derived and are then shown to be applicable to numerical solution of differential-difference equations arising from linear birth-death processes.
O'donohoe, M R, Murphy, J A
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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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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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Continued $\mathbf{A_2}$-fractions and singular functions
Математичні Студії, 2022 In the article we deepen the metric component of theory of infinite $A_2$-continued fractions $[0;a_1,a_2,...,a_n,...]$ with a two-element alphabet $A_2=\{\frac12,1\}$, $a_n\in A_2$ and establish the normal property of numbers of the segment $I=[\frac12 ...
M.V. Pratsiovytyi +3 more
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Continued fractions for some transcendental numbers [PDF]
, 2015 We consider series of the form $p/q + \sum_{j=2}^\infty 1/x_j$, where $x_1=q$ and the integer sequence $x_n$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for n?1.
Andrew N. W. Hone, Hone, Andrew N.W.
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ON SMARANDACHE GENERAL CONTINUED FRACTIONS [PDF]
, 1995 The continued fraction is called a Smarandache general continued fraction associated with A and ...
Maohua, Le
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ON SMARANDACHE SIMPLE CONTINUED FRACTIONS [PDF]
, 1999 Starting with a Smarandache type sequence, showing that if A is a positive integer sequence, then the simple continued fraction is ...
Ashbacher, Charles, Le, Maohua
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