The multipole expansion for small source region and far field R0 is mainly discussed in this paper.By applying the uniform three-dimensional generalized Taylor expansion and vector operator ▽ theory,a serial of electrical charge multipole and electric current multipole conclusions are deduced.The multipole matrix expression and multipole expansion of four-dimensional electric current vector in relativity are discussed.Concept is clear,deduction is standardized and conclusion is simple.The matrix expression is an attempt to multipole expansion theory.