How to capitalize the first letter of the first word in the argument of "\section"?

Question

I want to capitalize the first letter of the first word in the argument of a "\section" \command.

Consider \newcommand{\hello}{hello world}

I want to use

\section{\hello} 

so that the compiled section header is

0.1 Hello world  

I tried

\titleformat{\section}
   {\normalfont\Large\bfseries\expandafter\MakeUppercase }{\thesection}{1em}{}

But that returns HELLO WORLD.

How can I only capitalize the first word so that I get

0.1 Hello world  

Is there a way to carry over the title to the table of contents as well?

\let\TEMPtableofcontents\tableofcontents
\renewcommand{\tableofcontents}{
  \clearemptydoublepage
  \providecommand\phantomsection{} \phantomsection
  \addcontentsline{toc}{chapter}{Table of Contents}
  \TEMPtableofcontents
}

Answer 1

A simpler version of Skillmon's answer. This should work with every class that has the standard syntax for \section.

\documentclass{article}
\ExplSyntaxOn
\cs_new_eq:NN \titlecasefirst \text_titlecase_first:n
\ExplSyntaxOff
\NewCommandCopy{\latexsection}{\section}
\RenewDocumentCommand{\section}{sO{#3}m}{%
  \IfBooleanTF{#1}{%
    \latexsection*{\titlecasefirst{#3}}
  }{%
    \latexsection[\titlecasefirst{#2}]{\titlecasefirst{#3}}%
  }%
}
\newcommand{\hello}{hello world}
\begin{document}
\tableofcontents
\section{\hello}
\section[again \hello]{Again \hello{} but much longer}
\end{document}

Answer 2

The following works with a (more or less) up to date LaTeX installation.

\documentclass{article}
\ExplSyntaxOn
\cs_new_eq:NN \titlecasefirst \text_titlecase_first:n
\ExplSyntaxOff
\usepackage{titlesec}
\titleformat{\section}
  {\normalfont\Large\bfseries}{\thesection}{1em}{\titlecasefirst}
\newcommand{\hello}{hello world}
\begin{document}
\section{\hello}
\end{document}

But the ToC will not contained the altered heading. To also get the ToC affected the following assumes more or less standard-class behaviour.

It patches the macro formatting section-entries in the Toc (\l@section) to alter its argument to the result as if \section{\protect\titlecasefirst{<title>}} was always used instead of \section{<title>}.

\documentclass{article}
\ExplSyntaxOn
\cs_new_eq:NN \titlecasefirst \text_titlecase_first:n
\ExplSyntaxOff
\usepackage{titlesec}
\titleformat{\section}
  {\normalfont\Large\bfseries}{\thesection}{1em}{\titlecasefirst}
\makeatletter
\AtBeginDocument
  {%
    \NewCommandCopy\l@section@orig\l@section
    \renewcommand\l@section[1]
      {%
        \expandafter\l@section@orig\expanded
          {{\iffalse{{\fi\l@section@titlecasefirst#1}}}}%
      }%
  }
\newcommand\l@section@titlecasefirst[2]
  {%
    \unexpanded{#1{#2}}%
    \unexpanded\expandafter
      {\expandafter\titlecasefirst\expandafter{\iffalse}}\fi
  }
\makeatother
\newcommand{\hello}{hello world}
\begin{document}
\tableofcontents
\section{\hello}
\end{document}

Answer 3

Here's a LuaLaTeX-based solution. No knowledege of Lua (the programming language) is assumed or needed. It works for the table of contents as well as for the main body of the document. It works not only for the arguments of \section direcives, but also for those of \subsection and \subsubsection commands.

If you're new to LuaLaTeX, the only notable changes you'll need to apply to your preamb is (a) to make sure that the fontenc and \inputenc packages are not loaded and (b) the fontspec package is loaded.

% !TEX TS-program = lualatex
\documentclass{report}      % or some other suitable document class
\setcounter{secnumdepth}{3} % just for this sample document 
\setcounter{tocdepth}{3}
\usepackage{luacode}
% Define two Lua functions:
\begin{luacode}

function makefirstcap ( s )
   return ( string.upper ( s:sub (1,1) ) .. s:sub ( 2 ) )
end
function first2cap  ( s )
   s = tostring ( s )
   s = s:gsub ( "(\\.-section)%s*{%s*(.-)}" , 
                function ( x , y )
                   return ( x .."{".. makefirstcap ( y ) .. "}" ) 
                end )
   return s 
end

\end{luacode}

% Assign 'first2cap' function to LuaTeX's "process_input_buffer" callback
\AtBeginDocument{\directlua{luatexbase.add_to_callback (
   "process_input_buffer" , first2cap , "first2cap" )}}

\usepackage{fontspec} % don't load either fontenc or inputenc

\begin{document}

\tableofcontents
\bigskip\hrule\bigskip

\setcounter{chapter}{2} % just for this example

\section{hello world} 
\subsection {goodbye} \subsubsection{ the end} 
\subsubsection { what?! }
\end{document}