Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis
Fecha
2024-04-03
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MDPI
Resumen
Given a sequence of orthogonal polynomials
{
L
n
}
n
=
0
∞
, orthogonal with respect to a positive Borel
ν
measure supported on
R
+
, let
{
Q
n
}
n
=
0
∞
be the the sequence of orthogonal polynomials with respect to the modified measure
r
(
x
)
d
ν
(
x
)
, where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula
Q
n
(
d
)
(
z
)
L
n
(
d
)
(
z
)
⇉
n
∏
k
=
1
N
1
a
k
+
i
z
+
a
k
A
k
∏
j
=
1
N
2
z
+
b
j
b
j
+
i
B
j
, on compact subsets of
C
∖
R
+
, where
a
k
and
b
j
are the zeros and poles of r, and the
A
k
,
B
j
are their respective multiplicities
Descripción
Citación
Féliz-Sánchez, C.; Pijeira-Cabrera, H.; Quintero-Roba, J. Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis. Mathematics 2024, 12, 1082. https://doi.org/10.3390/math12071082
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