error_functions.py 文件源码

def _eval_aseries(self, n, args0, x, logx):
        point = args0[0]

        # Expansion at oo
        if point is S.Infinity:
            z = self.args[0]

            # expansion of C(x) = C1(x*sqrt(pi/2)), see reference[5] page 1-8
            p = [(-1)**k * C.factorial(4*k + 1) /
                 (2**(2*k + 2) * z**(4*k + 3) * 2**(2*k)*C.factorial(2*k))
                 for k in xrange(0, n)]
            q = [1/(2*z)] + [(-1)**k * C.factorial(4*k - 1) /
                 (2**(2*k + 1) * z**(4*k + 1) * 2**(2*k - 1)*C.factorial(2*k - 1))
                 for k in xrange(1, n)]

            p = [-sqrt(2/pi)*t for t in p] + [C.Order(1/z**n, x)]
            q = [ sqrt(2/pi)*t for t in q] + [C.Order(1/z**n, x)]

            return S.Half + (C.cos(z**2)*Add(*p) + C.sin(z**2)*Add(*q)).subs(x, sqrt(2/pi)*x)

        # All other points are not handled
        return super(fresnelc, self)._eval_aseries(n, args0, x, logx)


###############################################################################
#################### HELPER FUNCTIONS #########################################
###############################################################################