# Papers

## Published Papers

Generating k-Pell Infinite Series Using Whittaker’s Formula (Redirects to the website of “The Mathematics Enthusiast”) In this paper I introduce Whittaker’s method of finding the smallest absolute root of a polynomial and I apply it to a special class of polynomials. By applying Whittaker’s formula on these polynomial equations, we obtain infinite series for square roots of positive integers that involve integers belonging to specific k-Pell sequences.

## Website Papers

Representing Polynomials with Complex Coefficients using Lill’s Method This is a slightly shorter version of a paper I submitted to a journal. It shows how to represent polynomials with complex coefficients using Lill’s method.
Lill’s Method and the Sum of Arctangents
In this paper I have a detailed introduction to Lill’s method (only polynomials with real coefficients). I also prove a special property and show an application of that property.
Fibonacci Infinite Series and the Negative Powers of the Golden Ratio
This is an informal paper where I show 2 interesting infinite series formulas that converge to the negative powers of the golden ratio.
Lill’s Method and Graphical Solutions to Quadratic Equations
In this paper I go over a few methods that can be used to find the solutions to second degree polynomials with real coefficients. These methods are connected to Lill’s method.
Pell Infinite Series and the Negative Powers of the Silver Ratio
This paper is similar to my paper on the Fibonacci infinite series and the negative powers of the golden ratio. This paper points out that the formulas presented can probably be extended to all the metallic numbers.