I know the formulae for the test statistic for the Welch t-test and the degrees of freedom, as given on Wikipedia: https://en.wikipedia.org/wiki/Welch%27s_t-test
How can I go from these formulae to calculating the power of the test (i.e. probability we will end up rejecting $H_0$ given in fact $H_1$ is true) for a given $\delta$ (the difference between the two means)?
(It can be assumed that sample variances $s_1^2$, $s_2^2$ and numbers of observations $n_1$,$n_2$ are given, as is $\alpha$ for the test and that the test is two-tailed. The $H_0$ is that $\delta=0$.)