We explore a complex extension of finite calculus on the integer lattice of the complex plane. satisfies the discretized Cauchy–Riemann equations at if and . From this principle arise notions of the discrete path integral, Cauchy’s theorem, the exponential function, discrete analyticity, and falling power series.
"A complex finite calculus." Involve 3 (3) 273 - 287, 2010. https://doi.org/10.2140/involve.2010.3.273