  We first give a new proof and also a new formulation for the Abhyankar-Gurjar
inversion formula for formal maps of affine spaces. We then use the
reformulated Abhyankar-Gurjar formula to give a more straightforward proof for
the equivalence of the Jacobian Conjecture with a special case of the Vanishing
Conjecture of (homogeneous) quadratic differential operators with constant
coefficients.
