ON COMMON BOREL DIRECTIONS OF MEROMORPHIC FUNCTIONS OF INFINITE ORDER
Xiao Xiuzhi
G. Polya has proved the following theorem: suppose that G(Z) is an entire function of infinite order. If the order of G(Z) attains that of the entire complex plane, in any arbitary small angular domain whose bisector is some direction arg Z=_0, then arg Z=_0 is Julia direction of G(Z). In this article a characteristic theorem of Borel direction of meromorphic functions of infinite order is established, based on R. Nevanlinna's fundamental inequality for angular domains. It may be applied to common Borel direction of the functions and their multiple values, of the constants and "low order" functions, of the functions and their derivatives. One of the main theorems is: Theorem. Among the meromorphic functions of infinite order of the complex plane, any function f(Z) and it's reciprocal 1/(f(Z)) have at least one, it's Borel direction of the order p(r) with Borel direction of the order p(r) of the derivative is common.


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