M. Lassalle. Une formule du binome g'en'eralis'ee pour les polynomes de Jack. C. R. Acad. Sci. Paris, t. S'eries I, 310:253--256, 1990. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Non-Symmetric Jack Polynomials and Integral Kernels - Baker, Forrester (10 citations) (Correct)
....is seen to be in precise agreement with (3.43) 18 3.3 Evaluation of e p 1 (x) KA (x; y) and generalized binomial coefficients In the theory of the generalized hypergeometric function 0 F 0 (x; y) the identity 0 F 0 (x; y) 0 F 0 (x; y 1) 3. 50) is an immediate consequence of the identity [17, 20] (z) z) 3.51) with the generalized binomial coefficients defined by (1 z) i j C oe (z) oe (1 : 3.52) Analogous results hold for the function KA (x; y) although it is the analogue of (3.50) which is derived directly. KA (x; y) KA (x; y 1) ....
M. Lassalle. Une formule du binome g'en'eralis'ee pour les polynomes de Jack. C. R. Acad. Sci. Paris, t. S'eries I, 310:253--256, 1990.
The Calogero-Sutherland Model And Generalized Classical.. - Baker, Forrester (1997) (6 citations) (Correct)
....(N Gamma (i Gamma 1) ff(j Gamma 1) 2. 15) We have also used the notation (i) 1 ; i Gamma1 ; i Gamma 1; i 1 ; N ) 1 ; i Gamma1 ; i 1; i 1 ; N ) note that this is the opposite of what is used in [27, 17] but rather is that used by [20]) The polynomials in (2.11) are referred to as generalized Hermite, Laguerre and Jacobi polynomials respectively [14] they are uniquely specified up to normalization as the eigenfunctions of the operators (2.1) with an expansion in terms of Jack polynomials with highest weight (i.e. largest ....
....result in Lassalle s researches is an explicit formula for the action of the operator E 0 (recall (2.13a) the superscript (y) indicates operation with respect to the variables y) on 0 F 0 : 0 (2y; z) where p 1 (z) z j : 3.3) This formula follows from (2. 13a) and the result [17, 20] p 1 (x) C 1 (i) x) 3.4) Now in the notation of (2.12) the operator (2.1a) is given by = D 0 Gamma 2E 1 (3.5) Knowledge of the action of D 0 on 0 F 0 (2y; z) is required to prove Proposition 3.1. Lassalle uses the formulas (2.13) and (3.3) to establish this action. We ....
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M. Lassalle. Une formule du binome g'en'eralis'ee pour les polynomes de Jack. C. R. Acad. Sci. Paris, t. S'eries I, 310:253--256, 1990.
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