Before revision:  This yields a leading order expansion for the implied volatility at large strikes: BS( k,T)^{2}T\sim \Psi (s ^* -1) \times k (Roger Lee's moment formula).
After revision:  This yields a leading order expansion for the implied volatility at large strikes: BS( k,T)^{2}T\sim \Psi (s _+ -1) \times k (Roger Lee's moment formula).