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Statements
W
′
(
-
1
2
μ
2
,
μ
t
2
)
∼
-
μ
2
l
(
μ
)
(
t
2
+
1
)
1
4
(
sin
σ
¯
∑
s
=
0
∞
(
-
1
)
s
v
¯
2
s
(
t
)
(
t
2
+
1
)
3
s
μ
4
s
+
cos
σ
¯
∑
s
=
0
∞
(
-
1
)
s
v
¯
2
s
+
1
(
t
)
(
t
2
+
1
)
3
s
+
3
2
μ
4
s
+
2
)
,
asymptotic-expansion
diffop
parabolic-W
1
1
2
superscript
𝜇
2
𝜇
𝑡
2
𝜇
2
𝑙
𝜇
superscript
superscript
𝑡
2
1
1
4
¯
𝜎
superscript
subscript
𝑠
0
superscript
1
𝑠
subscript
¯
𝑣
2
𝑠
𝑡
superscript
superscript
𝑡
2
1
3
𝑠
superscript
𝜇
4
𝑠
¯
𝜎
superscript
subscript
𝑠
0
superscript
1
𝑠
subscript
¯
𝑣
2
𝑠
1
𝑡
superscript
superscript
𝑡
2
1
3
𝑠
3
2
superscript
𝜇
4
𝑠
2
{\displaystyle{\displaystyle W'\left(-\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right)%
\sim-\frac{\mu}{\sqrt{2}}l(\mu)(t^{2}+1)^{\frac{1}{4}}\left(\sin\overline{%
\sigma}\sum_{s=0}^{\infty}\frac{(-1)^{s}\overline{v}_{2s}(t)}{(t^{2}+1)^{3s}%
\mu^{4s}}+\cos\overline{\sigma}\sum_{s=0}^{\infty}\frac{(-1)^{s}\overline{v}_{%
2s+1}(t)}{(t^{2}+1)^{3s+\frac{3}{2}}\mu^{4s+2}}\right),}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
W
(
a
,
x
)
parabolic-W
𝑎
𝑥
{\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
s
𝑠
{\displaystyle{\displaystyle s}}
v
¯
s
(
t
)
subscript
¯
𝑣
𝑠
𝑡
{\displaystyle{\displaystyle\overline{v}_{s}(t)}}
σ
𝜎
{\displaystyle{\displaystyle\sigma}}
l
(
μ
)
𝑙
𝜇
{\displaystyle{\displaystyle l(\mu)}}
σ
¯
¯
𝜎
{\displaystyle{\displaystyle\overline{\sigma}}}
Identifiers
