Simpler expression for an operation on an ordered set

Question

Let $Q(A, b)$ denote an operation which takes as arguments an ordered set of integers $A$ and another integer $b$. For example let $A = \{x, y, z \}$, then

$$Q(A, b) = \frac{((b+x)\cdot b+y)\cdot b+z}{b^{|A|}}$$

My questions are:

• Is there a better notation for the operation $Q(A, b)$? I would like to be able to state it without an example, but I'm having trouble expressing it in product- or sum-notation.
• Is there anything we can say about $Q(A, b)$ without needing to calculate it first as stated above, i.e. a simpler expression or closed form?

Answer 1

$\Pi${ x + b : x in A } for the numerator.