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Statements
Ai
′
(
-
z
)
=
(
z
/
3
)
(
J
2
/
3
(
ζ
)
-
J
-
2
/
3
(
ζ
)
)
=
1
2
(
z
/
3
)
(
e
-
π
i
/
6
H
2
/
3
(
1
)
(
ζ
)
+
e
π
i
/
6
H
2
/
3
(
2
)
(
ζ
)
)
=
1
2
(
z
/
3
)
(
e
-
5
π
i
/
6
H
-
2
/
3
(
1
)
(
ζ
)
+
e
5
π
i
/
6
H
-
2
/
3
(
2
)
(
ζ
)
)
,
diffop
Airy-Ai
1
𝑧
𝑧
3
Bessel-J
2
3
𝜁
Bessel-J
2
3
𝜁
1
2
𝑧
3
superscript
𝑒
𝜋
𝑖
6
Hankel-H-1-Bessel-third-kind
2
3
𝜁
superscript
𝑒
𝜋
𝑖
6
Hankel-H-2-Bessel-third-kind
2
3
𝜁
1
2
𝑧
3
superscript
𝑒
5
𝜋
𝑖
6
Hankel-H-1-Bessel-third-kind
2
3
𝜁
superscript
𝑒
5
𝜋
𝑖
6
Hankel-H-2-Bessel-third-kind
2
3
𝜁
{\displaystyle{\displaystyle\mathrm{Ai}'\left(-z\right)=(z/3)\left(J_{2/3}%
\left(\zeta\right)-J_{-2/3}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})%
\left(e^{-\pi i/6}{H^{(1)}_{2/3}}\left(\zeta\right)+e^{\pi i/6}{H^{(2)}_{2/3}}%
\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{-5\pi i/6}{H^{(1)}_%
{-2/3}}\left(\zeta\right)+e^{5\pi i/6}{H^{(2)}_{-2/3}}\left(\zeta\right)\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)}}
H
ν
(
1
)
(
z
)
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
H
ν
(
2
)
(
z
)
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
Identifiers
