Two families of constant term identities
In 1985, Bressoud and Goulden derived the formula for the constant term in ∏ ( i , j ) ∈ T x j x i ∏ 0 ≤ i < j ≤ n ( x i x j ) a i ( q x j x i ) a j - 1 , where T ⊆ { ( i , j ) ∣ 0 ≤ i < j ≤ n } . This result implies the Andrews’ q -Dyson identity. In 2006, Gessel and Xin proved the q -Dyson i...
Saved in:
Published in | The Ramanujan journal Vol. 58; no. 3; pp. 701 - 722 |
---|---|
Main Author | |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.07.2022
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | In 1985, Bressoud and Goulden derived the formula for the constant term in
∏
(
i
,
j
)
∈
T
x
j
x
i
∏
0
≤
i
<
j
≤
n
(
x
i
x
j
)
a
i
(
q
x
j
x
i
)
a
j
-
1
, where
T
⊆
{
(
i
,
j
)
∣
0
≤
i
<
j
≤
n
}
. This result implies the Andrews’
q
-Dyson identity. In 2006, Gessel and Xin proved the
q
-Dyson identity by considering both sides of the equality as polynomials in
q
a
0
. We use this approach to determine the coefficients of
x
0
/
x
1
and
x
0
/
x
2
in Laurent polynomials studied by Bressoud and Goulden. |
---|---|
ISSN: | 1382-4090 1572-9303 |
DOI: | 10.1007/s11139-022-00569-1 |