def analytical_rate(td):
'''
Returns the dimensionless production rate
Input:
td: np.array(n)
Array of dimensionless times
Returns:
qd: np.array(n)
Array of dimensionless production rates
'''
pi = np.pi
term1 = 2*np.exp(-pi**2*td/4.)
term2 = erfc(1.5*pi*np.sqrt(td))/np.sqrt(pi*td)
return term1 + term2
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