Eisenstein Series, Alternative Modular Bases and Approximations of 1/π1/\pi

In this article using the theory of Eisenstein series, we give rise to the complete evaluation of two Gauss hypergeometric functions. Moreover we evaluate the modulus of each of these functions and the values of the functions in terms of the complete elliptic integral of the first kind. As application we give way of how to evaluate the parameters, in a closed-well posed form, of a general Ramanujan type $1/\pi$ formula. The result is a formula of 110 digits per term.Comment: Elliptic Functions; P

Note on a Nonlinear Differential Equation

We give evaluations in closed form of certain non linear differential equationsComment: Nonlinear Differential Equation

Evaluations of Ramanujan Continued Fractions

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 approximations, using Mathematica. In this way we produce new formulas and give new ideas for to prove new theorems.Comment: 8 page

On the Evaluation of the Fifth Degree Elliptic Singular Moduli

We find in a algebraic radicals way the value of singular moduli $k_{25^nr_0}$ for any integer $n$ knowing only two consecutive values $k_{r_0}$ and $k_{r_0/25}$Comment: 10 pages; Singular Moduli; Algebraic Numbers; Ramanujan; Continued Fractions; Elliptic Functions; Modular equations; Iterations; Polynomials; P

Algebraic Equations Solved with Jacobi Elliptic Functions

In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic singular modulus $k$.Comment: Quintic, Elliptic function

Evaluations of Derivatives of Jacobi Theta Functions in the origin

In this article using Ramanujan's theory of Eisenstein series we evaluate completely the derivatives of the theta functions $\vartheta_1^{(2\nu+1)}(z)$ and $\vartheta_4^{(2\nu)}(z)$ in the origin in closed polynomials forms using only the first three Eisenstein series of weights 2,4, and 6.Comment: 9 page

An Asymptotic relation for Hadjicostas Formula

We derive an asymptotic formula which in some cases generalize Hadjicostas formulaComment: 3 page

A General Method for Constructing Ramanujan Formulas for 1/πν1/\pi^{\nu}

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 elliptic alpha function whose values are useful for such evaluations.Comment: pi formulas, Ramanujan, 12 page

The Zenon effect in Quantum Mechanics

The basis of the so-called Zenon effect in Quantum Mechanics, is the limiting behavior of the unitary solution of Schroedinger's equation, under repeated measurments. We examine the limit of a sequence of operators complosed by a usual operator and a projection operator.Comment: 21 page

Research note on a well posed integral used in Apery's proof for the irrationality of Z(3)

In this note we evaluate multiple integrals that play a crucial role in the theory of irrationality of zeta functionComment: 4 page