A note on the fractional derivatives of a general system of polynomials
In this interesting paper the author has obtained the fractional derivative of a general system of polynomials \(S^ q_ n(z)\). The following is the main result obtained in this paper: \[ _ cD^ v_ zz^{\alpha}S^ q_ n(z)=\frac{z^{\alpha}(z-c)^{-v}}{\Gamma (l- v)}\sum^{[n/q]}_{r=0}(-n)_{qr}A(n,r)z^ r/r!_ 2F_ 1(-\alpha - r,-v;l-v;\frac{z-c}\quad {z}) \] which holds true for all values of v, where \(q\geq 1\), and A(n,r) is any arbitrary sequence. Certain special cases of the above result have also been given.
scientific article; zbMATH DE number 3923131