Section 20.5 Looking Ahead
Let's recap.The average value of
was-
The average value of
was-
Because of Euler's amazing solution to the Basel problem, we know that
so the constant in question is
-
a
is the coefficient and n
is the power of a model xxxxxxxxxx
def L(n):
ls = []
out = 0
for i in range(1,n+1):
out += euler_phi(i)
ls.append((i,out/i))
return ls
LS = L(1000)
P = line(LS)
def _(a=.01,n=2,view=(50,[25,50,..500])):
show(P+plot(a*x^n,0,view, color='black',linestyle="--"), xmin=1,xmax=view, ymax=LS[view][1])
pretty_print(html(r"Blue is the average value of $\phi$"))
pretty_print(html("Red is $%s x^{%s}$"%(latex(a),n)))