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Orthogonal polynomials associated to a certain fourth order differential equation

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Orthogonal polynomials associated to a certain fourth order differential equation. / Hilgert, Joachim; Kobayashi, Toshiyuki; Mano, Gen; Möllers, Jan.

I: Ramanujan Journal, Bind 26, Nr. 3, 2011, s. 295-310.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Hilgert, J, Kobayashi, T, Mano, G & Möllers, J 2011, 'Orthogonal polynomials associated to a certain fourth order differential equation', Ramanujan Journal, bind 26, nr. 3, s. 295-310. https://doi.org/10.1007/s11139-011-9338-6

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Author

Hilgert, Joachim ; Kobayashi, Toshiyuki ; Mano, Gen ; Möllers, Jan. / Orthogonal polynomials associated to a certain fourth order differential equation. I: Ramanujan Journal. 2011 ; Bind 26, Nr. 3. s. 295-310.

Bibtex

@article{931a366ea409416f9c737e58cae3af6d,
title = "Orthogonal polynomials associated to a certain fourth order differential equation",
abstract = "We introduce orthogonal polynomials $M_j^{\mu,\ell}(x)$ as eigenfunctions of a certain self-adjoint fourth order differential operator depending on two parameters $\mu\in\mathbb{C}$ and $\ell\in\mathbb{N}_0$.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 $L_j^\mu(x)$ for $\ell=0$.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.",
author = "Joachim Hilgert and Toshiyuki Kobayashi and Gen Mano and Jan M{\"o}llers",
year = "2011",
doi = "10.1007/s11139-011-9338-6",
language = "English",
volume = "26",
pages = "295--310",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer New York LLC",
number = "3",

}

RIS

TY - JOUR

T1 - Orthogonal polynomials associated to a certain fourth order differential equation

AU - Hilgert, Joachim

AU - Kobayashi, Toshiyuki

AU - Mano, Gen

AU - Möllers, Jan

PY - 2011

Y1 - 2011

N2 - We introduce orthogonal polynomials $M_j^{\mu,\ell}(x)$ as eigenfunctions of a certain self-adjoint fourth order differential operator depending on two parameters $\mu\in\mathbb{C}$ and $\ell\in\mathbb{N}_0$.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 $L_j^\mu(x)$ for $\ell=0$.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.

AB - We introduce orthogonal polynomials $M_j^{\mu,\ell}(x)$ as eigenfunctions of a certain self-adjoint fourth order differential operator depending on two parameters $\mu\in\mathbb{C}$ and $\ell\in\mathbb{N}_0$.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 $L_j^\mu(x)$ for $\ell=0$.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.

U2 - 10.1007/s11139-011-9338-6

DO - 10.1007/s11139-011-9338-6

M3 - Journal article

VL - 26

SP - 295

EP - 310

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 3

ER -