Higher Order Real Derivatives Using Parabolic Analytic Functions

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Konuralp Journal of Mathematics
Volume:11 Issue: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 : 91 | Download : 84

Publication Date : 2023-10-31

Article Type : Research Paper

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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