def b88_dg(x,b=0.0042): num = 6*b*b*x*x*(x/sqrt(x*x+1)-arcsinh(x))-2*b*x denom = pow(1+6*b*x*arcsinh(x),2) return num/denom
def b88_g(x,b=0.0042): return -1.5*pow(3./4./pi,1./3.)-b*x*x/(1.+6.*b*x*arcsinh(x))