Dominating Sequential Functions in Context of Nonelementary and Hypergeometric Functions

Abstract

Function plays an important role in mathematics and indefinite integration (i.e. antiderivative) provides the opportunity to create and propound new functions. Special functions like hypergeometric function, error function, exponential function etc. are useful as a tool of expressing many elementary and nonelementary functions as well as nonelementary integrals. In this paper we have studied the relations between dominating sequential and hypergeometric functions in context of nonelementary functions. The dominating sequential functions contain the extended dominating sequential trigonometric, dominating sequential hyperbolic, dominating sequential exponential and dominating sequential logarithmic functions. The dominating sequential functions have been expressed in terms of hypergeometric functions. A relation between dominating sequential and nonelementary functions has been discussed and found that no general relation exists between them except for some particular examples in terms of antiderivative. Also there doesn’t exist any direct or indirect relation between sequential and nonelementary function. The paper ends with a short note on limitations of the work and the future scope of research based on this paper.