On harmonic analysis related with the generalized Dunkl operator

Darboux transformations for Dunkl-Schroedinger equations with energy dependent potential and position dependent mass

“…Dunkl operators [9] are commuting differential-difference operators associated with finite reflection groups. As generalizations of partial derivatives, these operators appear in a wide range of mathematical applications, such as Fourier analysis related to root systems [2], intertwining operator and angular momentum algebra [12] [11], integrable Calogero-Moser-Sutherland (CMS) models [24] [10], harmonic analysis [5], the generation of orthogonal polynomials [17], and nonlinear wave equations [18]. Another field of application arises in quantum physics when conventional derivatives are replaced by Dunkl operators.…”

Some new results for Horn's hypergeometric functions Γ 1 and Γ 2

“…Recently, Opps et al [11,12] obtained recursion formulas for Appell's function F 2 . Brychkov [2] and Brychkov et al [3][4][5][6] gave the recursion formulas for Appell's hypergeometric functions F 1 , F 2 , F 3 and F 4 . Brychkov and Savischenko [7] obtained some formulas for Horn functions H 1 (a, b, c; d; w, z) and H (c) 1 (a, b; d; w, z).…”