Khitri-Kazi-Tani, Leila; Dib, Hacen A new \(h\)-discrete fractional operator, fractional power and finite summation of hypergeometric polynomials. (English) Zbl 1504.26016 Mem. Differ. Equ. Math. Phys. 86, 85-96 (2022). Summary: In the present paper, we introduce the discrete fractional trapezoidal operators \(T_h^{\alpha}\) for \(\alpha \in (0,1)\) as the fractional power of the classical trapezoidal formula. Consequently, we derive the fractional power of a triangular matrix. As applications, we determine the eigenvectors of \(T_h^{\alpha}\) and a finite summation formula of the product of hypergeometric polynomials. MSC: 26A33 Fractional derivatives and integrals 15A16 Matrix exponential and similar functions of matrices 33C05 Classical hypergeometric functions, \({}_2F_1\) 39A12 Discrete version of topics in analysis 47B12 Sectorial operators Keywords:discrete fractional calculus; trapezoidal operator; hypergeometric polynomials; sectorial operator; fractional power; matrix function; Meixner polynomials PDFBibTeX XMLCite \textit{L. Khitri-Kazi-Tani} and \textit{H. Dib}, Mem. Differ. Equ. Math. Phys. 86, 85--96 (2022; Zbl 1504.26016) Full Text: Link