Symbolic evaluation of Fourier series coefficients

from sympy import *
init_printing(pretty_print=True,use_latex=True)
%matplotlib inline
import matplotlib.pyplot as plt

f,t,T,G = symbols('f t T G')

f = G*t
print('f = ', f)

f =  G*t

plot((f.subs(G,25),(t,0,1)),((f-25).subs(G,25),(t,1,2)),((f-50).subs(G,25),(t,2,3)), ylabel='f = 25 t [V]',xlabel='t [sec]',xlim = (0,3))

<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x724ebbea3290>

c0 = integrate(f,(t,0,T))*(1/T)
print(c0) 
print(c0.subs([(G,25),(T,1)]))

G*T/2
25/2

a1 = (2/T)*integrate(f*sin(2*pi*t),(t,0,T))

print(a1)
print(a1.subs([(T,1),(pi, 3.14),(G,25)]))

2*G*(-T*cos(2*pi*T)/(2*pi) + sin(2*pi*T)/(4*pi**2))/T
-7.96178343949045

a,b = [],[]
for n in range(10):
    a.append((2/T)*integrate(f*sin(n*pi*t),(t,0,T)))
    b.append((2/T)*integrate(f*cos(n*pi*t),(t,0,T)))

a[9], b[9]

c = []
for n in range(1,10):
    print(a[n])
    expr = (a[n]**2 + b[n]**2)
    expr = expr.subs([(T,1),(pi, 3.14),(G,25)])
    # print expr
    # val = lambdify(t,expr,'numpy')
    c.append(expr)

2*G*(-T*cos(pi*T)/pi + sin(pi*T)/pi**2)/T
2*G*(-T*cos(2*pi*T)/(2*pi) + sin(2*pi*T)/(4*pi**2))/T
2*G*(-T*cos(3*pi*T)/(3*pi) + sin(3*pi*T)/(9*pi**2))/T
2*G*(-T*cos(4*pi*T)/(4*pi) + sin(4*pi*T)/(16*pi**2))/T
2*G*(-T*cos(5*pi*T)/(5*pi) + sin(5*pi*T)/(25*pi**2))/T
2*G*(-T*cos(6*pi*T)/(6*pi) + sin(6*pi*T)/(36*pi**2))/T
2*G*(-T*cos(7*pi*T)/(7*pi) + sin(7*pi*T)/(49*pi**2))/T
2*G*(-T*cos(8*pi*T)/(8*pi) + sin(8*pi*T)/(64*pi**2))/T
2*G*(-T*cos(9*pi*T)/(9*pi) + sin(9*pi*T)/(81*pi**2))/T

plt.figure()
plt.bar(range(1,10),c)
plt.xlabel('n')
plt.ylabel('Fourier coefficients $a_n^2 + b_n^2$')

Text(0, 0.5, 'Fourier coefficients $a_n^2 + b_n^2$')