respectively. The expression [ n ] q x n − − 1 is then the q -analog and ∑ ∑ k = 1 n ( n k ) x n − − k h k − − 1 is the h -analog of the power rule for positive integral powers. The q-Taylor expansion allows for the definition of q -analogs of all of the usual functions, such as the sine function, whose q -derivative is the q -analog of cosine.