In[]:=
deploy
Wed 1 Sep 2021 13:09:03
Background for https://mathoverflow.net/a/402932/7655
In[]:=
F[s]=Sqrt1Product1+,{k,1,∞};ToRadicals@FullSimplify[PowerExpand[F[s]]]//TraditionalForm
2s
3
k
Out[]//TraditionalForm=
Γ1-
3
-2
3
s
Γ
3
2
3
s
+1Γ
2/3
(-1)
3
2
3
s
+1In[]:=
G[s_]=Sum+2s,{k,1,∞}
k
3
k
Out[]=
-RootSum1+2s+3#1+3+&,&
1
3
2
#1
3
#1
PolyGamma[0,-#1]
1+#1
In[]:=
NIntegrate[F[s]G[s],{s,0,∞},PrecisionGoal20,WorkingPrecision20]
Out[]=
1.9921805635607759019