Analytic Properties of the Quaternion Function

Many properties of complex functions are pretty difficult to be generalized in the field of quaternion function, as the commutative law of multiplication fails in the latter. The derivative of quaternion function is defined in this paper. Moreover, by the similar method in judging the analytic property of complex function, Cauchy-Riemann equation is used to determine the analytic property of quaternion function. Furthermore, several concrete examples are discussed, and certain errors in (P. W. Yang. 2009) are pointed out as well