## 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 *M*_{j}^{μ,l}(*x*) as eigenfunctions of a certain self-adjoint fourth order differential operator depending on two parameters μ ∈ **C** and *l* ∈ **N**_{0}.
These polynomials arise as *K*-finite vectors in the *L*^{2}-model of the minimal unitary representations of indefinite orthogonal groups, and reduce to the classical Laguerre polynomials *L*_{j}^{μ}(*x*) for *l* = 0.
We establish various recurrence relations and integral representations for our polynomials, as well as a closed formula for the *L*^{2}-norm. Further we show that they are uniquely determined as polynomial eigenfunctions.

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© Toshiyuki Kobayashi