A remark on the asymptotic expansion of density function of Wiener functionals

We consider the asymptotic expansion of density function of Wiener functionals as time tends to zero as in [S. Kusuoka, D.W. Stroock, Precise asymptotics of certain Wiener functionals, J. Funct. Anal. 99 (1991) 1–74], and give an explicit formula for the first coefficient.