A note on the fractional derivatives of a general system of polynomials
type: Item
instance of: scholarly article
title: A note on the fractional derivatives of a general system of polynomials
zbMATH Open document ID: 0577.33004
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 3923131
zbMATH Keywords: fractional integral
zbMATH Keywords: fractional derivative
zbMATH Keywords: system of polynomials
author: Ravinder Krishna Raina
reviewed by: K. C. Gupta
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3923131