The approximate functional equation gives an estimate for the size of the error term.
This scaling function itself is solution to a functional equation.
These functional equations are satisfied by the gamma function.
A simple form of functional equation is a recurrence relation.
Solving functional equations can be very difficult but there are some common methods of solving them.
The main method of solving elementary functional equations is substitution.
This yields the functional equation on the generating function :
The idea can even be generalised to situations where the variables don't refer to numbers at all, as in a functional equation.
In fact, this is no longer a recurrence relation but a functional equation.
This in turn leads to remarkable functional equations satisfied by f(z).
Wörterbuch für Mathematik