Elementary quartic functions and sets they form

We noted that exponential decomposition in series is divided into four series, which determine the elementary quartic functions: A (x) and C (x) (even), B (x) and D (x) (odd). Each of them can be considered as the 1st, 2nd or 3rd derivative of one of the others and as its own 4th derivative. These elements form real set of quartic functions (periodic, non-periodic and centauros, consisting of periodic and non-periodic parts). A comparison of the curves of the functions A(x) and C(x), B(x), and D(x) reveals an unusual phenomenon of their infinite mutual intersection (in the absence of inflections), conjugated with the periodicity of trigonometric functions. The four imaginary quartic elements are introduced in accordance with four real. Together they form a set of quartic complex functions, including not only ordinary ("trigonometric or Euler"), but also functions with other quartic composition. The introduction of four quartic elements of an imaginary argument easily explains the known and unknown connections between functions of real and of imaginary argument . The modification of the "quartic composition" of non-periodic and periodic functions of the quartic set, including usual, allow change their properties broadly and directionally. Numerical modeling reveals the most important and often unexpected features of functions related to a quartic set. Obviously, all of this explains the wide possibilities of applying quartic functions themselves in the field of theory and practice.