Basic Examples 
(5)
 

Compute
ψ(30)
:
In[117]:=
[◼]
ChebyshevPsi
[30]
Out[117]=
4Log[2]+3Log[3]+2Log[5]+Log[7]+Log[11]+Log[13]+Log[17]+Log[19]+Log[23]+Log[29]
———
Obtain a decimal approximation:
In[118]:=
[◼]
ChebyshevPsi
[30]//N
Out[118]=
28.4765
———
Plot
ψ(x)
from 0 to 30:
In[119]:=
Plot
[◼]
ChebyshevPsi
[x],{x,0,30}
Out[119]=
———
Compare
x
,
ψ(x)
, and
|x-ψ(x)|
:
In[128]:=
Plotx,
[◼]
ChebyshevPsi
[x],Absx-
[◼]
ChebyshevPsi
[x],{x,0,30},PlotLegends{"x","ψ(x)","|x-ψ(x)|"}
Out[128]=
x
ψ(x)
|x-ψ(x)|
———
Plot the ratio
ψ(x)
x
:
In[121]:=
Plot
[◼]
ChebyshevPsi
[x]x,{x,0,100}
Out[121]=