Diego Dominici, F. Marcellan,
"Truncated Hermite polynomials"
, Serie RISC Report Series, Nummer 22-10, RISC, JKU, Hagenberg, Linz, 8-2022, ISSN: 2791-4267
Original Titel:
Truncated Hermite polynomials
Sprache des Titels:
Englisch
Original Kurzfassung:
We define the family of truncated Hermite polynomials $P_{n}left( x;zright) $, orthogonal with respect to the linear functional [Lleft[ pright] = int_{-z}^{z} pleft( xright) e^{-x^{2}} ,dx. ] The connection of $P_{n}left( x;zright) $ with the Hermite and Rys polynomials is stated. The semiclassical character of $P_{n}left( x;zright) $ as polynomials of class $2$ is emphasized. As a consequence, several properties of $P_{n}left( x;zright) $ concerning the coefficients $gamma_{n}left( zright) $ in the three-term recurrence relation they satisfy as well as the moments and the Stieltjes function of $L$ are given. Ladder operators associated with the linear functional $L$, a holonomic differential equation (in $x)$ for the polynomials $P_{n}left( x;zright) $, and a nonlinear ODE for the functions $gamma_{n}left( zright) $ are deduced.
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