As long as you make it clear what you're doing (and as long as your audience knows any programming at all), you should be able to get your point across. or you can just write some pseudocode, and say 'let $a_i$ be the value of a after $i$ iterations of x'. For all natural numbers $n>0$, define $a_n$ as: For example, I want the solution, say u (x,y), that satisfies integrate u. I want the solution that obeys some constraint.

Then you might turn that into a sequence, and write: I am trying to solve a PDE in Mathematica, using the NDSolve function. The easiest way to do this is to use a recursive definition. Plotting with FOR loop in mathematica 1,449 views Forloop mathematica equationofmotion Plotting the data from 'FOR' loop in mathematica for the equation of motion. To talk about the effects of code purely mathematically, you effectively need to find a way to express it without directly talking about 'time'. So, under the strictest possible interpretation, this question doesn't make sense. Variables are not updated they are either set to a specific value, or they range over all values simultaneously: there is no 'updating', because there is no 'time'. In pure math, functions don't have 'side-effects'.

For loop mathematica