Introduction to Dominating Sequential Hypergeometric Elementary Functions

The paper propounds the dominating sequential hyper geometric elementary functions, which extends the elementary functions from their sequential and dominating sequential functions to the newly introduced functions using their hyper geometric function representation. Thus six types of new functions namely dominating sequential hyper geometric trigonometric functions, dominating sequential hyper geometric inverse trigonometric functions, dominating sequential hyper geometric hyperbolic functions, dominating sequential hyper geometric inverse hyperbolic functions, dominating sequential hyper geometric exponential functions and dominating sequential hyper geometric logarithmic functions have been introduced corresponding to each standard type of elementary functions. Such functions will play an important role in expressing no elementary integral functions and will explore the domains of functions to a new height.