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3b

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 # Q 3B



import numpy as np

from scipy.special import legendre

from scipy.integrate import quad



# 1. for m = n (= 6,say)


m=6

n=6


f1 = legendre(m) * legendre(n)


y = quad(f1, -1, 1)


print("\nIntegral Pm * Pn for m = n = 6 is:",y[0])        # Verifying that integral of P(m)*P(n) from -infinity to +infinity for m=n equals 2/(2m+1)

print("2/(2m + 1); m = 6 is = " ,2/(2*m + 1))


# 2. for  m  !=  n


m = 3

n = 2


f2 = legendre(m) * legendre(n)

y2 = quad(f2, -1, 1)                                # Verifying that integral of P(m)*P(n) from -infinity to +infinity for m!=n equals 0

print("\nIntegral Pm * Pn for m not = n is:",y2[0])

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