Morphism classification of a family of transcendent functions arising from pharmacokinetic modelling

Abstract

Many transcendental functions were constructed through finding closed-form solutions of algebraic or differential equations and become ubiquitous gradually with increasing awareness of applications in specific problems naturally arising from life science. Motivated by Lambert W function, a family of transcendent X functions was introduced recently to express the closed-form solutions of some nonlinear pharmacokinetic models. Unfortunately, its mathematical properties have not been completely studied. For the purposes of mathematical point of views and the use of wider applications, our objective in this paper is to characterize morphism classification of X functions at the scope of real branches.