You might think this would work:

```
import numpy as np
n = len(Tm)
t = np.empty(n)
t[0] = 0 # or whatever the initial condition is
t[1:] = Tm[1:] + (t[0:n-1] - Tm[1:])**(-tau[1:])
```

but it doesn’t: you can’t actually do recursion in numpy this way (since numpy calculates the whole RHS and then assigns it to the LHS).

So unless you can come up with a non-recursive version of this formula, you’re stuck with an explicit loop:

```
tt = np.empty(n)
tt[0] = 0.
for i in range(1,n):
tt[i] = Tm[i] + (tt[i-1] - Tm[i])**(-tau[i])
```