Higher Order Real Derivatives Using Parabolic Analytic Functions

Year 2023, Volume: 11 Issue: 2, 141 - 147, 31.10.2023

Sandipan Dutta , Sneha Gupta

Abstract

Amid the bidimensional hypercomplex numbers, parabolic numbers are defined as $\{z=x+\imath y:\; x,y\in \mathbb{R}, \imath^2=0, \imath\neq 0\}$. The analytic functions of a parabolic variable have been introduced as an analytic continuation of the real function of a real variable. Also, their algebraic property has already been discussed. This paper will show the $n$-th derivative of the real functions using parabolic numbers to further generalize the automatic differentiation. Also, we shall show some of the applications of it.

Keywords

Parabolic, Analytic functions, Dual number, Higher order derivative, automatic differentiation, Hypercomplex numbers.

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