The value of expression
exp1=Re-
139
2
π
180
+8
2
Log
1
2
+
5
2

-3PolyLog2,-
4
-1+
5
2
+16PolyLog2,
2
-1+
5
2
π
3

-2PolyLog2,
4
-1+
5
2
π
3

+4PolyLog2,-
2
-1+
5
2
2ArcTan
1
7


+8PolyLog2,
2
-1+
5
2
2ArcTan
1
7


+4πArcTan
1
7
-12
2
ArcTan
1
7


is
2
2
π
15
It is easy to prove that exp1 is equal to
exp2=-
139
2
π
180
+4πArcTan
1
7
-12
2
ArcTan
1
7

+8
2
Log
1
2
+
5
2

-3PolyLog2,-
4
-1+
5
2
+4Sum
1
n^2
(-1)^n
2n
-1+
5
2
Cos2nArcTan
1
7
,{n,1,Infinity}+8Sum
1
n^2
2n
-1+
5
2
Cos2nArcTan
1
7
,{n,1,∞}-2Sum
4n
-1+
5
2
Cos
nπ
3

2
n
,{n,1,Infinity}+16Sum
2n
-1+
5
2
Cos
nπ
3

2
n
,{n,1,∞};
In[]:=
N[exp1,50]==N
2
2
π
15
,50
Out[]=
True
In[]:=
N[exp2,50]==N
2
2
π
15
,50
Out[]=
True
In[]:=
exp1===
2
2
π
15
Out[]=
False
Myquestionishowcanexp1(orexp2)besimplifiedtoobtain
2
2
π
15