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Statements
B
2
m
+
1
2
n
+
1
(
q
)
B
1
2
n
+
1
(
q
)
=
(
-
1
)
m
(
(
1
2
)
m
+
1
)
2
(
q
4
)
m
+
1
2
(
1
+
O
(
m
-
1
)
)
w
I
(
1
2
π
;
b
2
n
+
1
(
q
)
,
q
)
,
subscript
superscript
𝐵
2
𝑛
1
2
𝑚
1
𝑞
subscript
superscript
𝐵
2
𝑛
1
1
𝑞
superscript
1
𝑚
superscript
Pochhammer
1
2
𝑚
1
2
superscript
𝑞
4
𝑚
1
2
1
Big-O
superscript
𝑚
1
subscript
𝑤
I
1
2
𝜋
Mathieu-eigenvalue-b
2
𝑛
1
𝑞
𝑞
{\displaystyle{\displaystyle\frac{B^{2n+1}_{2m+1}(q)}{B^{2n+1}_{1}(q)}=\frac{(%
-1)^{m}}{\left({\left(\tfrac{1}{2}\right)_{m+1}}\right)^{2}}\left(\frac{q}{4}%
\right)^{m+1}\frac{2\left(1+O\left(m^{-1}\right)\right)}{w_{\mbox{\tiny I}}(%
\frac{1}{2}\pi;b_{2n+1}\left(q\right),q)},}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
b
n
(
q
)
Mathieu-eigenvalue-b
𝑛
𝑞
{\displaystyle{\displaystyle b_{\NVar{n}}\left(\NVar{q}\right)}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
π
{\displaystyle{\displaystyle\pi}}
m
𝑚
{\displaystyle{\displaystyle m}}
q
=
h
2
𝑞
superscript
ℎ
2
{\displaystyle{\displaystyle q=h^{2}}}
n
𝑛
{\displaystyle{\displaystyle n}}
w
I
(
z
;
a
,
q
)
subscript
𝑤
I
𝑧
𝑎
𝑞
{\displaystyle{\displaystyle w_{\mbox{\tiny I}}(z;a,q)}}
B
m
(
q
)
subscript
𝐵
𝑚
𝑞
{\displaystyle{\displaystyle B_{m}(q)}}
Identifiers
