Padé approximants and Eisenstein— Ramanujan continued fraction
نویسندگان
چکیده
منابع مشابه
A Continued Fraction of Ramanujan
In a manuscript discovered in 1976 by George E. Andrews, Ramanujan states a formula for a certain continued fraction, without proof. In this paper we establish formulae for the convergents to the continued fraction, from which Ramanujan's result is easily deduced.
متن کاملOn the Generalized Rogers–ramanujan Continued Fraction
On page 26 in his lost notebook, Ramanujan states an asymptotic formula for the generalized Rogers–Ramanujan continued fraction. This formula is proved and made slightly more precise. A second primary goal is to prove another continued fraction representation for the Rogers–Ramanujan continued fraction conjectured by R. Blecksmith and J. Brillhart. Two further entries in the lost notebook are e...
متن کاملThe Rogers-Ramanujan continued fraction and its level 13 analogue
One of the properties of the Rogers-Ramanujan continued fraction is its representation as an infinite product given by r(q) = q ∞ ∏
متن کاملRamanujan and the Regular Continued Fraction Expansion of Real Numbers
In some recent papers, the authors considered regular continued fractions of the form [a0; a, · · · , a } {{ } m , a, · · · , a } {{ } m , a, · · · , a } {{ } m , · · · ], where a0 ≥ 0, a ≥ 2 and m ≥ 1 are integers. The limits of such continued fractions, for general a and in the cases m = 1 and m = 2, were given as ratios of certain infinite series. However, these formulae can be derived from ...
متن کاملDynamics of a Continued Fraction of Ramanujan with Random Coefficients
We study a generalization of a continued fraction of Ramanujan with random, complexvalued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding c...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1992
ISSN: 0377-0427
DOI: 10.1016/0377-0427(92)90134-j