An introduction to complex functions on products of two time scales

Abstract

In this paper, we study the concept of analyticity for complex-valued functions of a complex time scale variable, derive a time scale counterpart of the classical Cauchy–Riemann equations, introduce complex line delta and nabla integrals along time scales curves, and obtain a time scale version of the classical Cauchy integral theorem.

Keywords:

• Time scales
• Delta analytic functions
• Time scale curves
• Complex line delta and nabla integrals
• Cauchy's integral theorem

Keywords:

• 30G25
• 30G30
• 39A10

Acknowledgement

Martin Bohner acknowledges financial support by a University of Missouri Research Board grant.

Notes

¶Email: [email protected]

Additional information

Notes on contributors

Gusein Sh. Guseinov

¶ ¶Email: [email protected]