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Statements
J
ν
′
(
ν
z
)
∼
-
2
z
(
1
-
z
2
4
ζ
)
1
4
(
Ai
(
ν
2
3
ζ
)
ν
4
3
∑
k
=
0
∞
C
k
(
ζ
)
ν
2
k
+
Ai
′
(
ν
2
3
ζ
)
ν
2
3
∑
k
=
0
∞
D
k
(
ζ
)
ν
2
k
)
,
asymptotic-expansion
diffop
Bessel-J
𝜈
1
𝜈
𝑧
2
𝑧
superscript
1
superscript
𝑧
2
4
𝜁
1
4
Airy-Ai
superscript
𝜈
2
3
𝜁
superscript
𝜈
4
3
superscript
subscript
𝑘
0
subscript
𝐶
𝑘
𝜁
superscript
𝜈
2
𝑘
diffop
Airy-Ai
1
superscript
𝜈
2
3
𝜁
superscript
𝜈
2
3
superscript
subscript
𝑘
0
subscript
𝐷
𝑘
𝜁
superscript
𝜈
2
𝑘
{\displaystyle{\displaystyle J_{\nu}'\left(\nu z\right)\sim-\frac{2}{z}\left(%
\frac{1-z^{2}}{4\zeta}\right)^{\frac{1}{4}}\*\left(\frac{\mathrm{Ai}\left(\nu^%
{\frac{2}{3}}\zeta\right)}{\nu^{\frac{4}{3}}}\sum_{k=0}^{\infty}\frac{C_{k}(%
\zeta)}{\nu^{2k}}+\frac{\mathrm{Ai}'\left(\nu^{\frac{2}{3}}\zeta\right)}{\nu^{%
\frac{2}{3}}}\sum_{k=0}^{\infty}\frac{D_{k}(\zeta)}{\nu^{2k}}\right),}}
Ai
(
z
)
Airy-Ai
𝑧
{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
ζ
(
z
)
𝜁
𝑧
{\displaystyle{\displaystyle\zeta(z)}}
C
k
(
ζ
)
subscript
𝐶
𝑘
𝜁
{\displaystyle{\displaystyle C_{k}(\zeta)}}
D
k
(
ζ
)
subscript
𝐷
𝑘
𝜁
{\displaystyle{\displaystyle D_{k}(\zeta)}}
Identifiers
