Derivatives and Holomorphic Functions

The definition of the derivative at ζ₀ of a function f: X → ℂ₂, X ⊂ ℂ₂, of a bicomplex variable ζis formally the same as for a function of a complex variable: (1) D ζ f ( ζ 0 ) = lim ζ → ζ 0 f ( ζ ) − f ( ζ 0 ) ζ − ζ 0 , ζ − ζ 0 ∉ O 2 . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137278/8fd7813b-1623-4fc8-85ee-4834d4e2e8ea/content/eq1052.tif"/>