Review of Dominating Elementary Functions and their Representation in terms of Hypergeometric Functions

Abstract

Hypergeometric functions plays an important role in special functions, which is a generalized form of a geometric series having the power series with the coefficients made of ratios of rational functions of constants. It isn’t only a solution of the second order linear ordinary differential equations that is frequently encountered in mathematical, physical, and engineering problems but also behaves as a tool of expressing many elementary and nonelementary functions as well as nonelementary integrals in its form. In this paper we have studied the nature of dominating elementary functions in context of hypergeometric functions. The dominating elementary functions contain the extended trigonometric, hyperbolic, exponential and logarithmic functions having their monomial argument with general exponent r, whole divided by a monomial having general exponent m. Some corrections have been found in the dominating trigonometric and hyperbolic functions, which have been mentioned.  The dominating elementary functions have been expressed directly or indirectly in terms of hypergeometric functions. The paper ends with a short note on limitations of the work and the future scope of research based on this paper.