Integration of Bicomplex Valued Function along Hyperbolic Curve

TL;DR

This paper develops a theory for integrating bicomplex valued functions along hyperbolic paths, establishing a bicomplex analogue of the Fundamental Theorem of Calculus for line integrals.

Contribution

It introduces bicomplex valued functions of bounded variations, defines integration over hyperbolic paths, and proves a fundamental theorem analogous to classical calculus.

Findings

Defined bicomplex functions of bounded variation

Established integration over rectifiable hyperbolic paths

Proved bicomplex Fundamental Theorem of Calculus for line integrals

Abstract

In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex functions over rectifiable hyperbolic path. Also we have established bicomplex analogue of the Fundamental Theorem of Calculus for line integral.