Suppose $X \sim N(0, \sigma^2)$, is it possible to evaluate $E[\Phi(\frac{aX + b}{c}) | X > k]$ in closed form, where $\Phi$ is the standard normal cdf?

The motivation comes from that it is possible to evaluate something like $E[\Phi(\frac{aX + b}{c})]$ with a closed-form expression. But not sure if something similar holds for the conditional expectation case.

Thanks!

Suppose $X \sim N(0, \sigma^2)$, is it possible to evaluate $E[\Phi(\frac{aX + b}{c}) | X > k]$ in closed form, where $\Phi$ is the standard normal cdf?

The motivation comes from that it is possible to evaluate something like $E[\Phi(\frac{aX + b}{c})]$ with a closed-form expression. But not sure if something similar holds for the conditional expectation case.