A characterization of entire functions of order one and infinite type is given and is used to generalize Hankel's formula. Using Green's functions and generalized Green's functions, an integral representation of 2{dollar}pi{dollar}-periodic and trigonometrically convex functions which are indicators of holomorphic functions of non-zero finite order is given. A representation for functions--satisfying certain growth conditions--which are in the closure of the linear span of a nonfundamental sequence is also given.
展开▼
机译：给出了一阶和无限类型的整个函数的刻画，并将其用于推广汉克尔公式。使用格林函数和广义格林函数，给出了2 {pial} pi {dollar}-周期和三角凸函数的积分表示，它们是非零有限阶全纯函数的指标。还给出了功能描述（满足某些增长条件），这些条件在非基本序列的线性跨度的封闭中给出。
展开▼
