On the fractional calculus of a general class of polynomials
By applying the expansion formula \[ (x+\xi)^{-\lambda}= \xi^{-\lambda} \sum^\infty_{n=0} {(\lambda)_n\over n!} (-x/\xi)^n, \] and the familiar fractional derivative formula \[ D^q_x x^h={\Gamma(1+h)\over \Gamma(1+h-q)} x^{h-q}\quad (\text{Re} h>-1), \] the authors obtain expressions for \[ D^\mu_x\{x^k(x+\xi)^{-\lambda} S^m_n(x^\rho(x+\xi)^{-\sigma}),\qquad\text{and} \] \[ D^\mu_x\{x^k(x+\xi)^{-\lambda} S^m_n(x^\rho(x+\xi)^{-\sigma}) S^q_p(x^\delta)\}, \] where \(S^m_n\) denotes the system of polynomials due to \textit{H. M. Srivastava} [Ind. J. Math. 14, 1-6 (1972; Zbl 0249.33006)]. Special cases are briefly treated.
scientific article; zbMATH DE number 941304