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Statements
∫
0
∞
t
μ
-
ν
-
1
𝐇
ν
(
t
)
d
t
=
Γ
(
1
2
μ
)
2
μ
-
ν
-
1
tan
(
1
2
π
μ
)
Γ
(
ν
-
1
2
μ
+
1
)
,
superscript
subscript
0
superscript
𝑡
𝜇
𝜈
1
Struve-H
𝜈
𝑡
𝑡
Euler-Gamma
1
2
𝜇
superscript
2
𝜇
𝜈
1
1
2
𝜋
𝜇
Euler-Gamma
𝜈
1
2
𝜇
1
{\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu-\nu-1}\mathbf{H}_{\nu}%
\left(t\right)\mathrm{d}t=\frac{\Gamma\left(\tfrac{1}{2}\mu\right)2^{\mu-\nu-1%
}\tan\left(\tfrac{1}{2}\pi\mu\right)}{\Gamma\left(\nu-\tfrac{1}{2}\mu+1\right)%
},}}
|
ℜ
μ
|
<
1
𝜇
1
{\displaystyle{\displaystyle|\Re\mu|<1}}
ℜ
ν
>
ℜ
μ
-
3
2
𝜈
𝜇
3
2
{\displaystyle{\displaystyle\Re\nu>\Re\mu-\tfrac{3}{2}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
𝐇
ν
(
z
)
Struve-H
𝜈
𝑧
{\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
tan
z
𝑧
{\displaystyle{\displaystyle\tan\NVar{z}}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
