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Statements
𝗃
n
(
z
)
=
(
-
i
)
n
2
∫
0
π
e
i
z
cos
θ
P
n
(
cos
θ
)
sin
θ
d
θ
.
spherical-Bessel-J
𝑛
𝑧
superscript
𝑖
𝑛
2
superscript
subscript
0
𝜋
superscript
𝑒
𝑖
𝑧
𝜃
shorthand-Legendre-P-first-kind
𝑛
𝜃
𝜃
𝜃
{\displaystyle{\displaystyle\mathsf{j}_{n}\left(z\right)=\frac{(-i)^{n}}{2}%
\int_{0}^{\pi}e^{iz\cos\theta}P_{n}\left(\cos\theta\right)\sin\theta\mathrm{d}%
\theta.}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
P
ν
(
z
)
=
P
ν
0
(
z
)
shorthand-Legendre-P-first-kind
𝜈
𝑧
Legendre-P-first-kind
0
𝜈
𝑧
{\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}%
\left(z\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
𝗃
n
(
z
)
spherical-Bessel-J
𝑛
𝑧
{\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
