Related papers: A Direct Proof of Landen's Transformation

In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.

The rational Landen transformation is a map on the coefficients of a rational integrand that preserves the value of the integral. This is the rational analog of the classical Landen transformations for elliptic integrals that leads to the…

We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closed-form expressions for a large class of integrals of even rational functions and to develop an algorithm…

The rational Landen transformation is a map on the space of coefficients of a rational integrand that preserves the value of the integral. We provide a family of these transformations that apply to rational integrands on the whole line.…

A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.

We present a simple inductive proof of the Lagrange Inversion Formula.

The rational Landen transformations are used to produce a highly efficient numerical method for the integration of rational functions.

In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.

We establish an explicit form of the Backlund transformation for the most known integrable systems.

We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…

The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.

We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effective method for computing Weierstrass functions, their…

This paper presents a novel direct elementary proof for Fermat's Last Theorem. We use algebra, modular math, and binomial series to develop inherent mathematical relationships hidden within Fermat's Last Theorem. With these derived…

We prove a result on the existence of linear forms of a given Diophantine type.

In this note, we demonstrate a method to invert some Hankel matrices explicitly by using the kernel polynomials for the related classical orthogonal polynomials.

The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…

We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.