THE n/2-TH DERIVATIVE OF f(x)=cos px USING GAMMA FUNCTION

Abstract

This study presents the n/2-th derivative of cosine function f(x)=cos px where p is a positive integer and x is a variable. The n/2-th derivative is a fractional derivative of an arbitary order. The fractional derivative can be obtained by using Riemann-Lioville integral fractional definition that closely related to gamma function. We utilize some properties of gamma function to find the n/2-th derivative of cosine function.