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