Let H denote the skew field of real quaternions. Its elements are of the form q = x_0 + ix_1 + jx_2 + kx_3, where the x_1 are real and i, j, k are imaginary units (i.e., the square of each equals -1) such that ij= -ji = k, jk = -kj = i, and ki = -ik = j. The richness of the theory of holomorphic functions of one complex variable, along with motivations from physics, aroused a natural interest in a theory of quaternion-valued functions of a quaternionic variable. In fact, in the last century, several interesting theories have been introduced.
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