  The generalized Taylor expansion including a secret auxiliary parameter $h$
which can control and adjust the convergence region of the series is the
foundation of the homotopy analysis method proposed by Liao. The secret of $h$
can't be understood in the frame of the homotopy analysis method. This is a
serious shortcoming of Liao's method. We solve the problem. Through a detailed
study of a simple example, we show that the generalized Taylor expansion is
just the usual Taylor's expansion at different point $t_1$. We prove that there
is a relationship between $h$ and $t_1$, which reveals the meaning of $h$ and
the essence of the homotopy analysis method. As an important example, we study
the series solution of the Blasius equation. Using the series expansion method
at different points, we obtain the same result with liao's solution given by
the homotopy analysis method.
