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.
Parabolic Analytic functions Dual number Higher order derivative automatic differentiation Hypercomplex numbers.
Birincil Dil | İngilizce |
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Konular | Matematikte Kompleks Sistemler |
Bölüm | Articles |
Yazarlar | |
Yayımlanma Tarihi | 31 Ekim 2023 |
Gönderilme Tarihi | 18 Temmuz 2023 |
Kabul Tarihi | 21 Ekim 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 11 Sayı: 2 |