Generalised Airy polynomials
We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight ω ( x ; t , λ ) = x λ exp − 1 3 x 3 + t x , x ∈ R + with parameters λ > −1 and t ∈ R . We also investigate the zeros and recurrence coefficients of the polynomials. The generalised sextic F...
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Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2021-05, Vol.54 (18), p.185202 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight
ω
(
x
;
t
,
λ
)
=
x
λ
exp
−
1
3
x
3
+
t
x
,
x
∈
R
+
with parameters
λ
> −1 and
t
∈
R
. We also investigate the zeros and recurrence coefficients of the polynomials. The generalised sextic Freud weight
ω
(
x
;
t
,
λ
)
=
|
x
|
2
λ
+
1
exp
−
x
6
+
t
x
2
,
x
∈
R
arises from a symmetrisation of the generalised Airy weight and we study analogous properties of the polynomials orthogonal with respect to this weight. |
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ISSN: | 1751-8113 1751-8121 |
DOI: | 10.1088/1751-8121/abf019 |