Math line breaks in user defined macros

Question

I have been defining a mathematic formula using NewDocumentCommand. This works well, but I do manage to get line breaks.

A minimal working example can be found below. Part of the construction is borrowed from parse variable length comma separated list into command (Peter Grill's answer).

\documentclass{article}

\usepackage{amsmath}
\usepackage{pgffor}
\usepackage{xparse}

\NewDocumentCommand{\formulaEx}{m}{
    \gdef\separator{}
    \gdef\formula{}
    \foreach \x in {1,...,#1} {%
        \xdef\formula{\formula \separator \frac{1}{(1+\x)^{\x}} }
        \gdef\separator{ + }
    }
    \formula
    \gdef\formula{}
}

\begin{document}

\begin{align*}
 P &= \formulaEx{10}
\end{align*}

\end{document}

This does not generate any line break. Replacing + by + \\ or + \newline yields an error. I also tried to use the package breqn but it is ineffective (no error but no line break).

I have tried a number of workarounds (such as adapting the solution proposed here tex capacity exceeded when using breqn package with a separate macro), but all of them were useless.

Many thanks for your help.

Answer 1

It was token hell, but the hill was taken, sir.

\documentclass{article}
\usepackage{lipsum}
\usepackage{amsmath}
\usepackage{pgffor}
\usepackage{xparse}
\newcommand\addtoformula[1]{\global\formula\expandafter{\the\formula#1}}
\newcommand\exaddtoformula[1]{\expandafter\global\expandafter\addtoformula\expandafter{#1}}
\newtoks\formula
\newtoks\formx
\NewDocumentCommand{\formulaEx}{m}{
    \gdef\separator{}
    \formula{}
    \foreach \x in {1,...,#1} {%
      \exaddtoformula{\separator\allowbreak\dfrac{1}}%
      \formx{}%
      \formx\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter(%
        \expandafter\expandafter\expandafter1\expandafter\expandafter\expandafter+%
          \expandafter\x\expandafter)\expandafter^\expandafter{\x}}
      \expandafter\addtoformula\expandafter{\expandafter{\the\formx}}%
      \gdef\separator{ +\rule[-4ex]{0pt}{0pt}}% PROVIDES EXTRA INTERLINE VERTICAL SPACE
    }
    \the\formula\vspace{-2ex}% UNDOES EXTRA SPACE ON LAST LINE
}
\begin{document}
\lipsum[1]
\begin{center}
$P = \formulaEx{10}$
\end{center}
\lipsum[2]
\end{document}

Something of an aligned style presentation can be achieved by way of invocation as follows:

\begin{center}
$P = \parbox[t]{4in}{$\formulaEx{10}$}$
\end{center}

Of course, while I went through the effort to build the token list in the above solution, there is really no need to do so when pursuing things in inline mode, and one can, instead, output each fraction directly.

\documentclass{article}
\usepackage{lipsum}
\usepackage{amsmath}
\usepackage{pgffor}
\usepackage{xparse}
\NewDocumentCommand{\formulaEx}{m}{
    \gdef\separator{}
    \foreach \x in {1,...,#1} {%
      \separator \dfrac{1}{(1+\x)^{\x}} 
      \gdef\separator{ +\rule[-4ex]{0pt}{0pt}}% PROVIDES EXTRA INTERLINE VERTICAL SPACE
    }
    \vspace{-2ex}% UNDOES EXTRA SPACE ON LAST LINE
}
\begin{document}
\lipsum[1]
\begin{center}
$P = \formulaEx{10}$
\end{center}
\lipsum[2]
\end{document}

Answer 2

You can use breqn, if you wish. On the other hand, it takes more time to build this for the package than to type in the whole formula directly.

\documentclass{article}
\usepackage{breqn}
\usepackage{xparse}

\ExplSyntaxOn
\seq_new:N \l__isanco_formula_temp_seq

\NewDocumentCommand{\FormulaEx}{mmm}
 {% #1 = times to repeat, #2 = control sequence, #3 = formula
  \cs_set_protected:Nn \__isanco_formula_repeat:n { #3 }
  \int_step_inline:nnnn { 1 } { 1 } { #1 }
   {
    \seq_put_right:Nx \l__isanco_formula_temp_seq
     {
      \exp_not:o { \__isanco_formula_repeat:n { ##1 } }
     }
   }
  \tl_new:N #2
  \tl_set:Nx #2 { \seq_use:Nn \l__isanco_formula_temp_seq { + } }
 }
\ExplSyntaxOff

\FormulaEx{10}{\formulaA}{\frac{1}{(1+#1)^{#1}}}

\begin{document}

\begin{dmath*}
P=\formulaA
\end{dmath*}

\end{document}