  A physically more adequate definition of a quaternionic holomorphic
(H-holomorphic) function of one quaternionic variable compared to known ones
and a quaternionic generalization of Cauchy-Riemann's equations are presented.
At that a class of introduced H-holomorphic functions consists of those
quaternionic functions whose left and right derivatives become equal after the
transition to 3D space. The presented theory demonstrates a complete similarity
of the algebraic properties and differentiation rules between the classes of
H-holomorphic and ordinary complex holomorphic functions, including the fact
that quaternionic multiplication of the H-holomorphic functions behaves as
commutative and the fact that each H-holomorphic function can be created from
its complex holomorphic analogue by replacing a complex variable by a
quaternion one. A fairly large number of detailed examples are given to
illustrate the presented theory efficiency.
