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Statements
∫
-
∞
∞
e
i
b
t
𝗃
n
(
t
)
d
t
=
{
π
i
n
P
n
(
b
)
,
-
1
<
b
<
1
,
1
2
π
(
±
i
)
n
,
b
=
±
1
,
0
,
±
b
>
1
,
superscript
subscript
superscript
𝑒
𝑖
𝑏
𝑡
spherical-Bessel-J
𝑛
𝑡
𝑡
cases
𝜋
superscript
𝑖
𝑛
shorthand-Legendre-P-first-kind
𝑛
𝑏
1
𝑏
1
1
2
𝜋
superscript
plus-or-minus
imaginary-unit
𝑛
𝑏
plus-or-minus
1
0
plus-or-minus
𝑏
1
{\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{ibt}\mathsf{j}_{n}\left(%
t\right)\mathrm{d}t=\begin{cases}\pi i^{n}P_{n}\left(b\right),&-1<b<1,\\
\frac{1}{2}\pi(\pm\mathrm{i})^{n},&b=\pm 1,\\
0,&\pm b>1,\end{cases}}}
π
{\displaystyle{\displaystyle\pi}}
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)}}
𝗃
n
(
z
)
spherical-Bessel-J
𝑛
𝑧
{\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
