def f1(x):
"""
An angular integral that appears in electron noise calculation.
"""
term1 = x * (mp.si(x) - 0.5 * mp.si(2*x))
term2 = -2 * mp.sin(0.5 * x)**4
return (term1 + term2)/x**2
def f2(x):
"""
Another angular integral in electron noise calculation.
"""
term1 = 2*x**3 * (2*mp.si(2*x)-mp.si(x))
term2 = 2*x**2 * (mp.cos(2*x) - mp.cos(x))
term3 = x * (mp.sin(2*x) - 2*mp.sin(x)) - (mp.cos(2*x) - 4* mp.cos(x) + 3)
return (term1 + term2 + term3)/(12 * x**2)
def f63(x):
# Si
return mpmath.si(x)
