Searcharxiv⌕ Search

arXiv subjects

Nikos Bagis

Publications and source records attributed to Nikos Bagis.

At least 37 records · Page 2Linked to original sources
arXiv2012

Generalizations of Ramanujans Continued fractions

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 for certain cases of Ramanujan Quantities-(RQ). We also give the modular equations of degree 2 and 3 for the evaluation of the first derivative of Rogers-Ramanujan continued fraction. More precicely for certain classes of (RQ)'s we show how we can find the corresponding continued fraction expansions-S, in which we are able to evaluate with numerical methods some lower degree modular equations of this fraction and its derivatives. A systematicaly method for evaluating theoriticaly certain (RQ)'s (not for all) and their derivatives, with functions used by Ramanujan himself, is presented. We give applications and several results.

math.GM↗
arXiv2012

A General Method for Constructing Ramanujan Formulas for $1/π^ν$

In this article we give the theoretical background for generating Ramanujan type $1/π^{2ν}$ formulas. As applications of our method we give a general construction of $1/π^4$ series and examples of $1/π^6$ series. We also study the elliptic alpha function whose values are useful for such evaluations.

math.GM↗
arXiv2011

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 $\vartheta_1^{(2ν+1)}(z)$ and $\vartheta_4^{(2ν)}(z)$ in the origin in closed polynomials forms using only the first three Eisenstein series of weights 2,4, and 6.

math.GM↗
arXiv2011

The First Derivative of Ramanujans Cubic Continued Fraction

We give the complete evaluation of the first derivative of the Ramanujans cubic continued fraction using Elliptic functions. The Elliptic functions are easy to handle and give the results in terms of Gamma functions and radicals from tables.

math.GM↗
arXiv2010

Eisenstein Series, Alternative Modular Bases and Approximations of $1/π$

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 $1/π$ formula. The result is a formula of 110 digits per term.

math.GM↗
arXiv2010

Some Notes on the Solutions of non Homogeneous Differential Equations

We solve some forms of non homogeneous differential equations in one and two dimensions. By expanding the solution into whell-posed closed form-Eisenstein series the solution itself is quite simple and elementary. Also we consider Fourier series solutions of linear differential operator equations. In the third section we study operators which are functions of the Leibnitz derivative. The last result is the complete solution of a non homogenus 2-degree ODE with linear coeficients. The non homogenous part is an arbirtary function of $L_2(\bf R\rm)$

math.GM↗
arXiv2009

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.

math.GM↗
arXiv2009

The general solution of Schrodigers differential equation

In this note we solve theoretically the Schrodingers differential equation using results based on our previous work which concern semigroup operators. Our method does not use eigenvectors or eigenvalues and the solution depends only from the selected base of the Hilbert space.

math.GM↗
arXiv2009

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.

physics.gen-ph↗