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Statements
∫
0
π
/
2
𝐇
ν
(
z
sin
θ
)
(
sin
θ
)
ν
+
1
(
cos
θ
)
2
ν
d
θ
=
2
-
ν
π
Γ
(
1
2
-
ν
)
z
ν
-
1
(
1
-
cos
z
)
,
superscript
subscript
0
𝜋
2
Struve-H
𝜈
𝑧
𝜃
superscript
𝜃
𝜈
1
superscript
𝜃
2
𝜈
𝜃
superscript
2
𝜈
𝜋
Euler-Gamma
1
2
𝜈
superscript
𝑧
𝜈
1
1
𝑧
{\displaystyle{\displaystyle\int_{0}^{\pi/2}\mathbf{H}_{\nu}\left(z\sin\theta%
\right)\frac{(\sin\theta)^{\nu+1}}{(\cos\theta)^{2\nu}}\mathrm{d}\theta=\frac{%
2^{-\nu}}{\sqrt{\pi}}\Gamma\left(\tfrac{1}{2}-\nu\right)z^{\nu-1}(1-\cos z),}}
-
3
2
<
ℜ
ν
<
1
2
3
2
𝜈
1
2
{\displaystyle{\displaystyle-\tfrac{3}{2}<\Re\nu<\tfrac{1}{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}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
