On stopping times for the Wiener process

In the paper, the expectations $\mathbf M(\tau(a,b,c)+c)^\nu$, $-\infty<\nu<\infty$, are found where $\tau(a,b,c)$ is the first passage time of the Wiener process for a one-side bound $a+b(t+c)^{1/2}$.
A moment identity for stochastic integrals is proved which can be useful when studying the properties of Markov times.