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

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.