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Statements
I
1
(
x
)
=
ℳ
h
1
(
1
)
x
-
1
+
1
2
π
i
∫
ρ
-
i
∞
ρ
+
i
∞
x
-
z
Γ
(
1
-
z
)
ℳ
h
1
(
z
)
d
z
,
subscript
𝐼
1
𝑥
Mellin-transform
subscript
ℎ
1
1
superscript
𝑥
1
1
2
𝜋
𝑖
superscript
subscript
𝜌
𝑖
𝜌
𝑖
superscript
𝑥
𝑧
Euler-Gamma
1
𝑧
Mellin-transform
subscript
ℎ
1
𝑧
𝑧
{\displaystyle{\displaystyle I_{1}(x)=\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0%
mu \left(1\right)x^{-1}+\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_{1}\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}}
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
