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Statements
Ai
′
(
z
)
=
-
π
-
1
(
z
/
3
)
K
±
2
/
3
(
ζ
)
=
(
z
/
3
)
(
I
2
/
3
(
ζ
)
-
I
-
2
/
3
(
ζ
)
)
=
1
2
(
z
/
3
)
e
-
π
i
/
6
H
2
/
3
(
1
)
(
ζ
e
π
i
/
2
)
=
1
2
(
z
/
3
)
e
-
5
π
i
/
6
H
-
2
/
3
(
1
)
(
ζ
e
π
i
/
2
)
=
1
2
(
z
/
3
)
e
π
i
/
6
H
2
/
3
(
2
)
(
ζ
e
-
π
i
/
2
)
=
1
2
(
z
/
3
)
e
5
π
i
/
6
H
-
2
/
3
(
2
)
(
ζ
e
-
π
i
/
2
)
,
diffop
Airy-Ai
1
𝑧
superscript
𝜋
1
𝑧
3
modified-Bessel-second-kind
plus-or-minus
2
3
𝜁
𝑧
3
modified-Bessel-first-kind
2
3
𝜁
modified-Bessel-first-kind
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
2
1
2
𝑧
3
superscript
𝑒
5
𝜋
𝑖
6
Hankel-H-1-Bessel-third-kind
2
3
𝜁
superscript
𝑒
𝜋
𝑖
2
1
2
𝑧
3
superscript
𝑒
𝜋
𝑖
6
Hankel-H-2-Bessel-third-kind
2
3
𝜁
superscript
𝑒
𝜋
𝑖
2
1
2
𝑧
3
superscript
𝑒
5
𝜋
𝑖
6
Hankel-H-2-Bessel-third-kind
2
3
𝜁
superscript
𝑒
𝜋
𝑖
2
{\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\pi^{-1}(z/\sqrt{3})K_%
{\pm 2/3}\left(\zeta\right)=(z/3)\left(I_{2/3}\left(\zeta\right)-I_{-2/3}\left%
(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})e^{-\pi i/6}{H^{(1)}_{2/3}}\left(%
\zeta e^{\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{-5\pi i/6}{H^{(1)}_{-2/3}}%
\left(\zeta e^{\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{\pi i/6}{H^{(2)}_{2/%
3}}\left(\zeta e^{-\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{5\pi i/6}{H^{(2)%
}_{-2/3}}\left(\zeta e^{-\pi i/2}\right),}}
Ai
(
z
)
Airy-Ai
𝑧
{\displaystyle{\displaystyle\mathrm{Ai}\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}}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
Identifiers
