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