CAJ | 학술논문

对于复平面上的亚纯函数，推广通常的增长级为p阶增长级，引进本质有穷的概念，进而研究本质有穷的亚纯函数的Borel例外值的存在性。将通常意义下有限级全纯函数的Hadamard因子分解定理和关于整函数组的Borel定理推广到本质有穷的亚纯函数上来，在此基础上，将熟知的有限级亚纯函数的Borel例外值定理推广到本质有穷亚纯函数的情形。
대우복평면상적아순함수，추엄통상적증장급위p계증장급，인진본질유궁적개념，진이연구본질유궁적아순함수적Borel예외치적존재성。장통상의의하유한급전순함수적Hadamard인자분해정리화관우정함수조적Borel정리추엄도본질유궁적아순함수상래，재차기출상，장숙지적유한급아순함수적Borel예외치정리추엄도본질유궁아순함수적정형。
In this paper, we ifrst introduce the concept of essential ifnite generalizing the common order of growth to the p-order of growth for meromorphic functions. Then the existence of Borel exceptional values of essential ifnite meromorphic functions and their derivatives are investigated. The Hadamard theorem has been proved for essential finite meromorphic functions. Therefore the famous Borel theorem has been generalized to essential ifnite meromorphic functions too. Finally, the existence theorem of Picard exceptional values of meromorphic functions and their derivatives are generalized to the existence theorem of Borel exceptional values of essential ifnite meromorphic functions and their derivatives.