error_functions.py 文件源码

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

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

            # expansion of S(x) = S1(x*sqrt(pi/2)), see reference[5] page 1-8
            p = [(-1)**k * factorial(4*k + 1) /
                 (2**(2*k + 2) * z**(4*k + 3) * 2**(2*k)*factorial(2*k))
                 for k in range(0, n)]
            q = [1/(2*z)] + [(-1)**k * factorial(4*k - 1) /
                 (2**(2*k + 1) * z**(4*k + 1) * 2**(2*k - 1)*factorial(2*k - 1))
                 for k in range(1, n)]

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

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

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