- Konuralp Journal of Mathematics
- Cilt: 11 Sayı: 2
- Higher Order Real Derivatives Using Parabolic Analytic Functions
Higher Order Real Derivatives Using Parabolic Analytic Functions
Authors : Sandipan Dutta, Sneha Gupta
Pages : 141-147
View : 62 | Download : 72
Publication Date : 2023-10-31
Article Type : Research
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.