Based on Getzler's rescaling transformation, we obtain a formula for the heat kernel coefficients of the Dirac Laplacian on a spin manifold. One can compute them explicitly up to an arbitrarily high order by using only a basic knowledge of calculus added to the formula.
"A formula for the heat kernel coefficients of the Dirac Laplacians on spin manifolds." Tsukuba J. Math. 45 (1) 69 - 81, July 2021. https://doi.org/10.21099/tkbjm/20214501069