Geodesic
An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 56-76.

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It is well known how to construct a system of symmetric orthogonal polynomials in an arbitrary finite number of variables from an arbitrary system of orthogonal polynomials on the real line. In the special case of the big $q$-Jacobi polynomials, the number of variables can be made infinite. As a result, in the algebra of symmetric functions, there arises an inhomogeneous basis whose elements are orthogonal with respect to some probability measure. This measure is defined on a certain space of infinite point configurations and hence determines a random point process.
Keywords: Big q-Jacobi polynomials, symmetric functions, Schur functions
Mots-clés : interpolation polynomials, beta distribution. 
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G. I. Olshanskii. An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 56-76. http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a3/

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