Integer Translation and Growth of Entire and Meromorphic Functions: Effect of Integer Translation on Growth of Composite Entire and Meromorphic Functions

The theory of entire and meromorphic functions is very important area of complex analysis. Finnish mathematician Rolf Nevanlinna (1926) initiated the value distribution theory for meromorphic functions which includes the theory of entire functions as a special case. In fact, this theory deals with the learning of the fact how an entire or meromorphic function assumes some values and the influence of assuming sure values in some explicit way on a function. Actually, the famous fundamental theorem of classical algebra is most likely the first value distribution theorem. The value distribution theory deals with the various features of the performance of entire and meromorphic functions, one of which is the study of comparative growth properties. On the other hand Serbian mathematician Jovan Karamata(1930) introduced the notion of a new class of functions called slowly increasing functions which have been applied in various fields of mathematics. In this book, the authors have tried to study some growth properties of integer translated composite entire and meromorphic functions with the effect of slowly increasing function and obtained a number of significant results.