Translator Disclaimer
2010 A complex finite calculus
Joseph Seaborn, Philip Mummert
Involve 3(3): 273-287 (2010). DOI: 10.2140/involve.2010.3.273

Abstract

We explore a complex extension of finite calculus on the integer lattice of the complex plane. f:[i] satisfies the discretized Cauchy–Riemann equations at z if Re(f(z+1)f(z))= Im(f(z+i)f(z)) and Re(f(z+i)f(z))=Im(f(z+1)f(z)). From this principle arise notions of the discrete path integral, Cauchy’s theorem, the exponential function, discrete analyticity, and falling power series.

Citation

Download Citation

Joseph Seaborn. Philip Mummert. "A complex finite calculus." Involve 3 (3) 273 - 287, 2010. https://doi.org/10.2140/involve.2010.3.273

Information

Received: 24 September 2009; Revised: 22 September 2010; Accepted: 23 September 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1203.30049
MathSciNet: MR2739519
Digital Object Identifier: 10.2140/involve.2010.3.273

Subjects:
Primary: 30G25, 39A12

Rights: Copyright © 2010 Mathematical Sciences Publishers

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.3 • No. 3 • 2010
MSP
Back to Top