Let ν be a finite measure on R whose Laplace transform is analytic in a neighborhood of zero. An anyon Lévy white noise on (R d , dx) is a certain family of noncommuting operators ω, ϕ in the anyon Fock space over L 2 (R d × R, dx ⊗ ν). Here ϕ = ϕ(x) runs over a space of test functions on R d , while ω = ω(x) is interpreted as an operator-valued distribution on R d . Let L 2 (τ ) be the noncommutative L 2 -space generated by the algebra of polynomials in variables ω, ϕ , where τ is the vacuum expectation state. We construct noncommutative orthogonal polynomials in L 2 (τ ) of the form P n (ω), f (n) , where f (n) is a test function on (R d ) n . Using these orthogonal polynomials, we derive a unitary isomorphism U between L 2 (τ ) and an extended anyon Fock space over dx)) if and only if the measure ν is concentrated at one point, i.e., in the Gaussian/Poisson case. Using the unitary isomorphism U , we realize the operators ω, ϕ as a Jacobi (i.e., tridiagonal) field in F(L 2 (R d , dx)). We derive a Meixner-type class of anyon Lévy white noise for which the respective Jacobi field in F(L 2 (R d , dx)) has a relatively simple structure. Each anyon Lévy white noise of the Meixner type is characterized by two parameters: λ ∈ R and η ≥ 0. Furthermore, we get the representation ω(x) = ∂ † x + λ∂ † x ∂ x + η∂ † x ∂ x ∂ x + ∂ x . Here ∂ x and ∂ † x are annihilation and creation operators at point x.

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line.

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