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DLMF:10.16#Ex5
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MaRDI QID
Q3858
Label: DLMF:10.16#Ex5
Digital Library of Mathematical Functions ID
10.16#Ex5
J
1
4
(
z
)
=
-
2
-
1
4
π
-
1
2
z
-
1
4
(
W
(
0
,
2
z
1
2
)
-
W
(
0
,
-
2
z
1
2
)
)
,
Bessel-J
1
4
𝑧
superscript
2
1
4
superscript
𝜋
1
2
superscript
𝑧
1
4
parabolic-W
0
2
superscript
𝑧
1
2
parabolic-W
0
2
superscript
𝑧
1
2
{\displaystyle{\displaystyle J_{\frac{1}{4}}\left(z\right)=-2^{-\frac{1}{4}}% \pi^{-\frac{1}{2}}z^{-\frac{1}{4}}\left(W\left(0,2z^{\frac{1}{2}}\right)-W% \left(0,-2z^{\frac{1}{2}}\right)\right),}}
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