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[en] Let ν be a finite measure on R whose Laplace transform is analytic in a neighbourhood of zero. An anyon L´evy white noise on (Rd,dx) is a certain family of noncommuting operators ⟨ω,ϕ⟩ on the anyon Fock space over L2(Rd ×R,dx⊗ν), where ϕ = ϕ(x) runs over a space of test functions on Rd, while ω = ω(x) is interpreted as an operator-valued distribution on Rd. Let L2(τ) be the noncommutative L2-space generated by the algebra of polynomials in the variables ⟨ω,ϕ⟩, where τ is the vacuum expectation state. Noncommutative orthogonal polynomials in L2(τ) of the form ⟨Pn(ω),f(n)⟩ are constructed, where f(n) is a test function on (Rd)n, and are then used to derive a unitary isomorphism U between L2(τ) and an extended anyon Fock space F(L2(Rd,dx)) over L2(Rd,dx). The usual anyon Fock space F(L2(Rd,dx)) over L2(Rd,dx) is a subspace of F(L2(Rd,dx)). Furthermore, the equality F(L2(Rd,dx)) = F(L2(Rd,dx)) holds if and only if the measure ν is concentrated at a single point, that is, in the Gaussian or Poisson case. With use of the unitary isomorphism U, the operators ⟨ω,ϕ⟩ are realized as a Jacobi (that is, tridiagonal) field in F(L2(Rd,dx)). A Meixner-type class of anyon L´evy white noise is derived for which the corresponding Jacobi field in F(L2(Rd,dx)) has a relatively simplestructure. EachanyonL´evywhitenoiseofMeixnertypeischaracterized by two parameters, λ ∈R and η > 0. In conclusion, the representation ω(x) = ∂† x + λ∂† x∂x + η∂† x∂x∂x + ∂x is obtained, where ∂x and ∂† x are the annihilation and creation operators at the point x.