Recent trends on the estimation of growth indicatiors of functions of complex variables

Abstract

newlineA function that is analytic at every point in the complex plane C is said to be an entire newlinefunction. A function that is analytic at every point of C except at points it has poles is newlinesaid to be meromorphic. Many commonly used functions are meromorphic such as the newlinetrigonometric and hyperbolic functions, elliptic functions, polynomials and rational func- newlinetions. The meromorphic function having an essential singularity at the point at in...nity is newlinecalled a transcendental meromorphic function. We will study the Value distribution the- newlineory of entire or meromorphic functions. In 1926 Finnish mathematician Rolf Nevanlinna newlineinitiated the Value distribution theory of entire or meromorphic functions which is also newlineknown as Nevanlinna Theory. The oldest result in the value distribution theory is the newlineFundamental Theory of Algebra (FTA) which states that If f is a polynomial of degree newlinen with real or complex coe¢ cients, then the equation f (z) = 0 has at least one root newlinewhere f be a complex valued function of a complex variable de...ned in the complex plane newlineC.