Answer by Symbol 1 for Plotting the sum of a function in TikZ

TL; DR, the function declaration should be

  \pgfmathdeclarefunction{manual_sum}{1}{%    \pgfmathfloattoint{#1}\let\cnt\pgfmathresult%    \pgfmathsetmacro\ret{0}%    \foreach\i in{1,...,\cnt}{%      \pgfmathsetmacro\ret{\ret+\i}         % summing integer itself     %\pgfmathsetmacro\ret{\ret+square(\i)} % general case      \xdef\ret{\ret}%    }%    \pgfmathparse{\ret}%  }

There are two problems in your code:

• First, \foreach introduces nested grouping and \ret is trapped in the group.
• Second, since pgfplots activates FPU, the \pgfmathtruncatemacro\cnt{#1} will make \cnt be 1.
  • (This is in fact the flag of #1 in the FPU representation.)
  • (flag1 stands for positive number.)

To come over the first obstacle, I usually use \xdef to smuggle the value. It is also worth noting that pgfplots introduces \pgfplotsforeachungrouped, which is literally an ungrouped version of \foreach.

For the second obstacle, one needs to check the manual carefully and finds that \pgfmathfloattoint{#1}\let\cnt\pgfmathresult is the correct way to do the job.

this will bring you a curve that is different from the explicit_sum, and then you will realize that #1*(#1-1)/2 is not the correct formula.