So, I was reading about power series solutions to differential equations and the author stressed how one should not bother trying to identify the final series solution with any closed form expression.
Now, he didn't really state that such a closed form will not exist for some series, he just insisted not to bother with trying to find one.
My question then is, is it so that some power series just DO NOT have closed form expressions no matter how hard we try to find or is it that theoretically we could find a complicated closed form expression to every series if we try hard enough?
EDIT: By closed form I mean some combination of elementary functions.