\contentsline {section}{\tocsection {}{1}{Introduction}}{2}
\contentsline {subsection}{\tocsubsection {}{1.1}{Polyz\^etas}}{2}
\contentsline {subsection}{\tocsubsection {}{1.2}{Polyz\^etas color\'es}}{3}
\contentsline {subsection}{\tocsubsection {}{1.3}{Polyz\^etas de Hurwitz}}{3}
\contentsline {section}{\tocsection {}{2}{Codage symbolique}}{4}
\contentsline {subsection}{\tocsubsection {}{2.1}{S\'eries non commutatives et int\'egrales it\'er\'ees}}{4}
\contentsline {subsection}{\tocsubsection {}{2.2}{S\'eries rationnelles}}{5}
\contentsline {subsection}{\tocsubsection {}{2.3}{Polylogarithmes}}{5}
\contentsline {subsection}{\tocsubsection {}{2.4}{Fonctions quasi-sym\'etriques}}{6}
\contentsline {subsection}{\tocsubsection {}{2.5}{Transform\'ee polylogarithmique}}{7}
\contentsline {section}{\tocsection {}{3}{R\'egularisation syntaxique des termes divergents}}{7}
\contentsline {subsection}{\tocsubsection {}{3.1}{R\'egularisation et s\'erie diagonale}}{8}
\contentsline {subsection}{\tocsubsection {}{3.2}{R\'egularisation syntaxique}}{9}
\contentsline {subsubsection}{\tocsubsubsection {}{3.2.1}{La r\'egularisation pour le premier m\'elange $\@mathsf {reg}_{\mathop {\scriptscriptstyle {\sqcup \tmspace -\thinmuskip {.1667em}\tmspace -\thinmuskip {.1667em}\sqcup }}}$}}{9}
\contentsline {subsection}{\tocsubsection {}{3.3}{Un exemple\nonbreakingspace : les int\'egrales d'Arakawa et Kaneko}}{11}
\contentsline {section}{\tocsection {}{4}{Polylogarithmes de Hurwitz}}{13}
\contentsline {subsection}{\tocsubsection {}{4.1}{D\'efinition et propri\'et\'es de base}}{13}
\contentsline {subsection}{\tocsubsection {}{4.2}{Premier codage des polyz\^etas de Hurwitz}}{14}
\contentsline {subsection}{\tocsubsection {}{4.3}{Deuxi\`eme codage des polyz\^etas de Hurwitz}}{15}
\contentsline {subsection}{\tocsubsection {}{4.4}{Troisi\`eme codage des polyz\^etas de Hurwitz}}{15}
\contentsline {subsection}{\tocsubsection {}{4.5}{R\'egularisation des polyz\^etas de Hurwitz divergents}}{16}
\contentsline {section}{\tocsection {}{5}{Polyz\^etas color\'es et Polyz\^etas de Hurwitz}}{18}
\contentsline {subsection}{\tocsubsection {}{5.1}{S\'eries g\'en\'eratrices de Dirichlet}}{18}
\contentsline {subsection}{\tocsubsection {}{5.2}{Polyz\^etas color\'es}}{19}
\contentsline {section}{\tocsection {}{}{References}}{20}