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Statements
I
2
(
x
)
=
∑
ℜ
β
0
≤
ℜ
z
≤
1
res
[
-
x
-
z
Γ
(
1
-
z
)
ℳ
h
2
(
z
)
]
+
1
2
π
i
∫
ρ
-
i
∞
ρ
+
i
∞
x
-
z
Γ
(
1
-
z
)
ℳ
h
2
(
z
)
d
z
.
subscript
𝐼
2
𝑥
subscript
subscript
𝛽
0
𝑧
1
residue
delimited-[]
superscript
𝑥
𝑧
Euler-Gamma
1
𝑧
Mellin-transform
subscript
ℎ
2
𝑧
1
2
𝜋
𝑖
superscript
subscript
𝜌
𝑖
𝜌
𝑖
superscript
𝑥
𝑧
Euler-Gamma
1
𝑧
Mellin-transform
subscript
ℎ
2
𝑧
𝑧
{\displaystyle{\displaystyle I_{2}(x)=\sum_{\Re\beta_{0}\leq\Re z\leq 1}%
\Residue\left[-x^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip
3%
.0mu \left(z\right)\right]+\frac{1}{2\pi i}\int_{\rho-i\infty}^{\rho+i\infty}x%
^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z%
\right)\mathrm{d}z.}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
ℳ
(
f
)
(
s
)
Mellin-transform
𝑓
𝑠
{\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
res
residue
{\displaystyle{\displaystyle\Residue}}
h
(
x
)
ℎ
𝑥
{\displaystyle{\displaystyle h(x)}}
I
j
(
x
)
subscript
𝐼
𝑗
𝑥
{\displaystyle{\displaystyle I_{j}(x)}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
Identifiers
