Orthogonal polynomials arising from the wreath products of a dihedral group with a symmetric group. (English) Zbl 1064.33009

Summary: Some classes of orthogonal polynomials are discussed in this paper which are expressed in terms of \((n+1,m+1)\)-hypergeometric functions. The orthogonality comes from that of zonal spherical functions of certain Gelfand pairs.


33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
05E35 Orthogonal polynomials (combinatorics) (MSC2000)
05E05 Symmetric functions and generalizations
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