The issue of constructing complicated quaternionic holomorphic (-holomorphic) functions in the Cayley-Dickson doubling form is considered. The way of -holomorphic substitutions, allowing us to construct -holomorphic composite functions of any degree of difficulty, is presented. The new –representation form for -holomorphic functions is established as a consequence of the earlier proved commutative behavior of the quaternionic multiplication in the case of -holomorühic functions. The specific polar form of -holomorphic functions with a real-valued modulus and argument similar to complex one is obtained. The -holomorphic generalizations of the logarithmic and inverse trigonometric and hyperbolic functions are implemented. The obtained results reaffirm that any complicated -holomorphic function can be constructed from its complex holomorphic analog. The processing of -holomorphic functions of any degree of difficulty is provided through high-speed programmes in system Wolfram Mathematica^® represented in the Appendix.

quaternionic analysis, quaternionic holomorphic functions, Cauchy-Riemann's equations, compositions of holomorphic functions, polar form, holomorphic logarithms, quaternionic inverse thigonometric and hyperbolic functions