相关论文: The First Derivative of Ramanujans Cubic Continued…
In this article we present ways to evaluate certain sums, products and continued fractions using tools from the theory of elliptic functions. The specific results appear to be new, although similar ones can be found in the leterature; in…
In this article we present evaluations of continued fractions studied by Ramanujan. More precisely we give the complete polynomial equations of Rogers-Ramanujan and other continued fractions, using tools from the elementary theory of the…
We study Ramanujan's cubic continued fraction and explicit evaluations of theta-functions
In this article with the help of the inverse function of the singular moduli we evaluate the Rogers Ranmanujan continued fraction and his first derivative.
In this paper we present experimental ways of evaluating Ramanujan`s quantities which as someone can see are related with algebraic numbers. The good thing with algebraic numbers is that can be found in a closed form, from there…
In this article we continue a previous work in which we have generalized the Rogers Ramanujan continued fraction (RR) introducing what we call, the Ramanujan-Quantities (RQ). We use the Mathematica package to give several modular equations…
We use some general properties, presented in previous work, to evaluate special cases of integrals relating Rogers-Ramanujan continued fraction, eta function and elliptic integrals.
Our main result is that any real cubic algebraic number has a continued fraction expansion with polynomial coefficients. Some generalizations are mentioned.
The periodic points of the algebraic function defined by the equation $g(x,y) = x^3(4y^2+2y+1)-y(y^2-y+1)$ are shown to be expressible in terms of Ramanujan's cubic continued fraction $c(\tau)$ with arguments in an imaginary quadratic field…
By using Euler's approach of using Euclid's algorithm to expand a power series into a continued fraction, we show how to derive Ramanujan's $q$-continued fractions in a systematic manner.
Ramanujan recorded four reciprocity formulas for the Roger-Ramanujan continued fraction. Two reciprocity formulas each are also associated with the Ramanujan--G\"ollnitz--Gordon continued fraction and a level-13 analog of the…
We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers--Ramanujan continued fraction play central roles in…
We present here a way to evaluate a very wide class of integrals relating Ramanujans continued fraction and q-product. To do this we explore briefily a differential equation, which relates these two functions
In this article we give the theoretical background for generating Ramanujan type $1/\pi^{2\nu}$ formulas. As applications of our method we give a general construction of $1/\pi^4$ series and examples of $1/\pi^6$ series. We also study the…
We study the properties of a general continued fraction of Ramanujan. In some certain cases we evaluate it completely.
Several continued fraction expansions for $e$ have been produced by an automated conjecture generator (ACG) called \emph{The Ramanujan Machine}. Some of these were already known, some have recently been proved and some remain unproven.…
In this paper, we represent a continued fraction expression of Mathieu series by a continued fraction formula of Ramanujan. As application, we obtain some new bounds for Mathieu series.
We suggest a continued fraction origin to Ramanujan's approximation to {(a-b)/(a+b)}^2 in terms of the arc length of an ellipse with semiaxes a and b. Moreover, we discuss the asymptotic accuracy of the approximation.
We derive continued fractions for partition generating functions, utilizing both Euler's techniques and Ramanujan's techniques. Although our results are for integer partitions there is scope to extend this work to vector partitions,…
This note discusses elliptic functions in Ramanujan's work.