Monday, November 14, 2016

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Note to readers:

I am presently writing a book about algebraic funtions covering the relevant concepts in the pages described below along with additional concepts and user guides to the supporting Mathematica notebooks. I hope to have the book completed sometime in $2025$ with tentative plans to publish it through Wolfram Media.

A website about algebraic functions and iterated exponential and polynomial systems

$$ \newcommand{\bint}{\displaystyle{\int\hspace{-10.4pt}\Large\mathit{8}}} \newcommand{\res}{\displaystyle{\text{Res}}} \newcommand{\wvalx}{\underbrace{z^{\lambda_4}(c_4+w_5)}_{w_4}} \newcommand{wvalxx}{\underbrace{z^{\lambda_3}(c_3+\wvalx)}_{w_3}} \newcommand{wvalxxx}{\underbrace{z^{\lambda_2}\{c_2+\wvalxx\}}_{w_2}} \newcommand{wvalxxxx}{z^{\lambda_1}\big(c_1+\wvalxxx\big)} $$

This web site is about algebraic functions $w(z)$ given implicitly by the expression $$ \begin{equation} f(z,w)=a_0(z)+a_1(z)w+a_2(z)w^2+\cdots+a_n(z)w^n=0 \label{eqn001} \end{equation} $$ with $z$ and $w$ complex variables and the coefficients, $a_i(z)$, polynomials in $z$ with rational coefficients; and iterated exponential and polynomial systems. Readers are advised to read the indicated background sections in order to better understand the content of each section.

The software used in this web site is Mathematica.

Algebraic functions:

Puiseux expansions around singular points and their radii of convergence:

Iterated exponential functions:

Folded polynomial functions:

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