#!/usr/bin/python
import sys,math
from ROOT import TH1D, TF1, TCanvas

m_e = 0.511
m_mu = 105.658
r = m_e/m_mu
z0 = 2*r/(1 + r**2)
L = 2*math.log(1/r)

def FBorn(x,p):
    z = 2*x[0]/(q + r**2)/m_mu
    v = math.sqrt(1 - m_e**2/x[0]**2)
    
    f = 6*(1 + r**2)**4 * v* z*(s *(1 - z) + 2/9 * 
                                p[0]*(4*z**2 - 3*z - z0**2) + 
                                p[1]*z0*(1 - z))
    return f

def f1(x,p):
    z = 2*x[0]/(q + r**2)/m_mu
    v = math.sqrt(1 - m_e**2/x[0]**2)

    li2 = TMath.DiLog(1 - z)

    fll1 = 5.6 + 2*z - 4*z**2 + 8/3*z**3 +  \
        2*z**2 *(3 - 2*z)*math.log( (1 - z)/z)
    R1 = -2*li2 + math.log(z)* math.log(1 - z) - 2*math.log(z)**2 -\
        math.log(1 - z)/z - 5/4
    f = (L - 1)*fll1 + 2*z**2*(3 - 2*z)*R1 + \
        (1 - z)/6*((10 + 34*z -32z**2) * math.log(z) + 5 - 27*z + 34*z**2)

    return f

def f2Llog(x,p):
    z = 2*x[0]/(q + r**2)/m_mu
    v = math.sqrt(1 - m_e**2/x[0]**2)
    
    Phi = TMath.DiLog(-(1 - z)/z) + math.log((1 - z)/z)**2 - TMath.Pi()**2/6

    f2ll = 4*z**2 *(3 - 2*z)*Phi + \
        (10.3 + 8*z - 16*z**2 + 32/3*z**3)*math.log(1 - z) + \
        (-5/6 - 2*z + 8*z**2 - 32/3*z**3)*math.log(z) + 11/36 + \
        17/6*z + 8/3*z**2 - 32/9*z**3

    f = (L - 1)**2/2 * f2ll

return f