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Statements
I
μ
f
(
x
)
=
∑
s
=
0
n
-
1
a
s
Γ
(
1
-
s
-
α
)
Γ
(
μ
+
1
-
s
-
α
)
x
μ
-
s
-
α
-
∑
s
=
1
n
c
s
Γ
(
μ
+
1
-
s
)
x
μ
-
s
+
1
x
n
δ
n
(
x
)
,
superscript
𝐼
𝜇
𝑓
𝑥
superscript
subscript
𝑠
0
𝑛
1
subscript
𝑎
𝑠
Euler-Gamma
1
𝑠
𝛼
Euler-Gamma
𝜇
1
𝑠
𝛼
superscript
𝑥
𝜇
𝑠
𝛼
superscript
subscript
𝑠
1
𝑛
subscript
𝑐
𝑠
Euler-Gamma
𝜇
1
𝑠
superscript
𝑥
𝜇
𝑠
1
superscript
𝑥
𝑛
subscript
𝛿
𝑛
𝑥
{\displaystyle{\displaystyle I^{\mu}f(x)=\sum_{s=0}^{n-1}a_{s}\frac{\Gamma%
\left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}x^{\mu-s-\alpha}-%
\sum_{s=1}^{n}\frac{c_{s}}{\Gamma\left(\mu+1-s\right)}x^{\mu-s}+\frac{1}{x^{n}%
}\delta_{n}(x),}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
I
μ
superscript
𝐼
𝜇
{\displaystyle{\displaystyle I^{\mu}}}
f
(
t
)
𝑓
𝑡
{\displaystyle{\displaystyle f(t)}}
n
𝑛
{\displaystyle{\displaystyle n}}
a
n
subscript
𝑎
𝑛
{\displaystyle{\displaystyle a_{n}}}
δ
n
(
x
)
subscript
𝛿
𝑛
𝑥
{\displaystyle{\displaystyle\delta_{n}(x)}}
c
s
subscript
𝑐
𝑠
{\displaystyle{\displaystyle c_{s}}}
