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All Journal Jambura Journal of Mathematics
Karim, Eka Mulyawati S.
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Mathematics

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Deret Maclaurin Turunan Fraksional Fungsi Inverse Trigonometri dan Radius Kekonverganannya Khoirunisa, Siti Miftahurrohmah; Anshori, Hafiz Iqbal; Karim, Eka Mulyawati S.
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.37016

Abstract

Fractional derivatives are a generalization of ordinary derivatives to non-integer or fractional orders. This study presents the fractional derivatives of inverse trigonometric functions (arcsin, arccos, and arctan) with the order constraint 0 α ≤ 1 . These inverse trigonometric functions are expressed in the form of Maclaurin series. Furthermore, their fractional derivatives can be determined using the Riemann–Liouville definition of fractional derivatives. The main results show an explicit formula for the fractional Maclaurin series and prove that the radius of convergence of the original function is equal to the radius of convergence of its fractional derivative.
Co-Authors Anshori, Hafiz Iqbal Khoirunisa, Siti Miftahurrohmah