J. Hilgert, T. Kobayashi, G. Mano, and J. Möllers, Orthogonal polynomials associated to a certain fourth order differential equation, Ramanujan Journal 26 (2011), 295-310, DOI: 10.1007/s11139-011-9338-6. arXiv:0907.2612 [math.CA]..

We introduce orthogonal polynomials Mjμ,l(x) as eigenfunctions of a certain self-adjoint fourth order differential operator depending on two parameters μ ∈ C and lN0. These polynomials arise as K-finite vectors in the L2-model of the minimal unitary representations of indefinite orthogonal groups, and reduce to the classical Laguerre polynomials Ljμ(x) for l = 0. We establish various recurrence relations and integral representations for our polynomials, as well as a closed formula for the L2-norm. Further we show that they are uniquely determined as polynomial eigenfunctions.

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