The Abel Theory of Power Series in Split-Complex Analysis

Abstract

The Split-complex number is a generalization of real number , which is a commutative ring with two zero divisors generated by two real numbers. In this paper, we first study the Abel theorem of power series and obtain root and ratio convergent criterion in split-complex analysis. Then this paper shows these regions of convergence by figures in split-complex space. Finally, from our perspective, the results presented in this work represent the extensions of the related ideas or findings in real analysis, which makes it possible to study them in a larger domain.