I have many problems trying to solve this one... tried the obvious, but did not work. It just append an empty function somehow.
array_of_functions.push(function() { first_function('a string') });
I solved it by using an array of strings, and later with eval:
array_of_functions.push("first_function('a string')");
for (var Func of array_of_functions) {
eval(Func);
}