|
|||||
 |
|
|
|
|
|
A complex finite
calculus
Joseph Seaborn and Philip Mummert
Vol. 3 (2010), No. 3, 273–287
|
Abstract |
|
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. |
Keywords
complex analysis, discrete analytic, finite calculus,
finite differences, monodiffric, preholomorphic, Gaussian
integers, integer lattice, discrete
|
Mathematical Subject Classification 2000
Primary: 30G25, 39A12
|
Milestones
Received: 24 September 2009
Revised: 22 September 2010
Accepted: 23 September 2010
Published: 16 October 2010
Proposed: Johnny Henderson
Communicated by Johnny Henderson
|
Authors |
| Joseph Seaborn | |
| Mathematics Department The University of North Carolina CB #3250, Phillips Hall 412 Chapel Hill, NC 27599 United States |
|
| Philip Mummert | |
| Mathematics Department Taylor University 236 W Reade Ave Upland, IN 46989 United States |
|
| http://faculty.taylor.edu/phmummert/ | |
|
