The Growth Of Taylor Series And Random Taylor Series

This paper is divided two large parts. In different parts, I have studied the growth and convergence of Taylor series and random Taylor series in the unit circle and the entire plane distinctively.The first part, a type-function and the order on the type-function are defined in the unit circle.Then the infinite order Taylor series in the unit circle is studied,and the relations between the order on the type-function and the coefficients of Taylor series are found.The second part, I have studied the growth and convergence of random Taylor series. In this paper,the order of growth and convergence of the random Taylor series are studied. Then at some certain conditions ,I gain the important results:the order of growth and convergence of the two kinds of random Taylor series are the same a.s..