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The Hi-Jack symmetric polynomials, which are associated with the simultaneouseigenstates for the first and second conserved operators of the quantumCalogero model, are studied. Using the algebraic properties of the Dunkloperators for the model, we derive the Rodrigues formula for the Hi-Jacksymmetric polynomials. Some properties of the Hi-Jack polynomials and therelationships with the Jack symmetric polynomials and with the basis given bythe QISM approach are presented. The Hi-Jack symmetric polynomials are strongcandidates for the orthogonal basis of the quantum Calogero model.Comment: 17 pages, LaTeX file using jpsj.sty (ver. 0.8), cite.sty,  subeqna.sty, subeqn.sty, jpsjbs1.sty and jpsjbs2.sty (all included.) You can  get all the macros from ftp.u-tokyo.ac.jp/pub/SOCIETY/JPSJ

Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model