Abstract: The analytic function is the basis of complex analysis, quaternion analysis, Clifford analysis as well as octonion analysis. It took many forms. The function is analytic function So long as after by the derivative operator. a simple has given in 1, but some mistakes. This article has pointed out its mistake through a counter-example. Moreover, in this paper, a more concise way is given(Theorem 1), And promoted it in octonion analysis(Theorem 2). Then we obtain an united formula to construct all kinds of analytic functions in complex analysis, quaternion analysis, Clifford analysis, and also in octonion analysis.