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Statements
Bi
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z
)
=
z
/
3
(
I
1
/
3
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ζ
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+
I
-
1
/
3
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ζ
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)
=
1
2
z
/
3
(
e
π
i
/
6
H
1
/
3
(
1
)
(
ζ
e
-
π
i
/
2
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+
e
-
π
i
/
6
H
1
/
3
(
2
)
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ζ
e
π
i
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2
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)
=
1
2
z
/
3
(
e
-
π
i
/
6
H
-
1
/
3
(
1
)
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ζ
e
-
π
i
/
2
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+
e
π
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H
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3
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2
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ζ
e
π
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,
Airy-Bi
𝑧
𝑧
3
modified-Bessel-first-kind
1
3
𝜁
modified-Bessel-first-kind
1
3
𝜁
1
2
𝑧
3
superscript
𝑒
𝜋
𝑖
6
Hankel-H-1-Bessel-third-kind
1
3
𝜁
superscript
𝑒
𝜋
𝑖
2
superscript
𝑒
𝜋
𝑖
6
Hankel-H-2-Bessel-third-kind
1
3
𝜁
superscript
𝑒
𝜋
𝑖
2
1
2
𝑧
3
superscript
𝑒
𝜋
𝑖
6
Hankel-H-1-Bessel-third-kind
1
3
𝜁
superscript
𝑒
𝜋
𝑖
2
superscript
𝑒
𝜋
𝑖
6
Hankel-H-2-Bessel-third-kind
1
3
𝜁
superscript
𝑒
𝜋
𝑖
2
{\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\sqrt{z/3}\left(I_{1/3}%
\left(\zeta\right)+I_{-1/3}\left(\zeta\right)\right)=\tfrac{1}{2}\sqrt{z/3}%
\left(e^{\pi i/6}{H^{(1)}_{1/3}}\left(\zeta e^{-\pi i/2}\right)+e^{-\pi i/6}{H%
^{(2)}_{1/3}}\left(\zeta e^{\pi i/2}\right)\right)=\tfrac{1}{2}\sqrt{z/3}\left%
(e^{-\pi i/6}{H^{(1)}_{-1/3}}\left(\zeta e^{-\pi i/2}\right)+e^{\pi i/6}{H^{(2%
)}_{-1/3}}\left(\zeta e^{\pi i/2}\right)\right),}}
Bi
(
z
)
Airy-Bi
𝑧
{\displaystyle{\displaystyle\mathrm{Bi}\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)}}
z
𝑧
{\displaystyle{\displaystyle z}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
Identifiers
