documentclass{article}
usepackage{amsmath}

newcommand{numberOfDocuments}{mathcal{N}}
newcommand{someSimpleCommand}{mathcal{F}}
newcommand{someComplexCommand}[1]{sum_{i = #1}^{#1+5} i}

begin{document}

This is $numberOfDocuments = 1$ document with equations
begin{align}
someSimpleCommand approx someComplexCommand{numberOfDocuments}
end{align}

end{document}

mathcal{N} = 1
mathcal{F} approx sum_{i = mathcal{N}}^{mathcal{N}+5} i