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Statements
a
m
(
h
2
)
b
m
+
1
(
h
2
)
}
∼
-
2
h
2
+
2
s
h
-
1
8
(
s
2
+
1
)
-
1
2
7
h
(
s
3
+
3
s
)
-
1
2
12
h
2
(
5
s
4
+
34
s
2
+
9
)
-
1
2
17
h
3
(
33
s
5
+
410
s
3
+
405
s
)
-
1
2
20
h
4
(
63
s
6
+
1260
s
4
+
2943
s
2
+
486
)
-
1
2
25
h
5
(
527
s
7
+
15617
s
5
+
69001
s
3
+
41607
s
)
+
⋯
.
asymptotic-expansion
selection
Mathieu-eigenvalue-a
𝑚
superscript
ℎ
2
Mathieu-eigenvalue-b
𝑚
1
superscript
ℎ
2
2
superscript
ℎ
2
2
𝑠
ℎ
1
8
superscript
𝑠
2
1
1
superscript
2
7
ℎ
superscript
𝑠
3
3
𝑠
1
superscript
2
12
superscript
ℎ
2
5
superscript
𝑠
4
34
superscript
𝑠
2
9
1
superscript
2
17
superscript
ℎ
3
33
superscript
𝑠
5
410
superscript
𝑠
3
405
𝑠
1
superscript
2
20
superscript
ℎ
4
63
superscript
𝑠
6
1260
superscript
𝑠
4
2943
superscript
𝑠
2
486
1
superscript
2
25
superscript
ℎ
5
527
superscript
𝑠
7
15617
superscript
𝑠
5
69001
superscript
𝑠
3
41607
𝑠
⋯
{\displaystyle{\displaystyle\rselection{a_{m}\left(h^{2}\right)\\
b_{m+1}\left(h^{2}\right)}\sim-2h^{2}+2sh-\frac{1}{8}(s^{2}+1)-\frac{1}{2^{7}h%
}(s^{3}+3s)-\frac{1}{2^{12}h^{2}}(5s^{4}+34s^{2}+9)-\frac{1}{2^{17}h^{3}}(33s^%
{5}+410s^{3}+405s)-\frac{1}{2^{20}h^{4}}(63s^{6}+1260s^{4}+2943s^{2}+486)-%
\frac{1}{2^{25}h^{5}}(527s^{7}+15617s^{5}+69001s^{3}+41607s)+\cdots.}}
a
n
(
q
)
Mathieu-eigenvalue-a
𝑛
𝑞
{\displaystyle{\displaystyle a_{\NVar{n}}\left(\NVar{q}\right)}}
b
n
(
q
)
Mathieu-eigenvalue-b
𝑛
𝑞
{\displaystyle{\displaystyle b_{\NVar{n}}\left(\NVar{q}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
Identifiers
