CCL: Slater orbital p - d transition probabilities

Help! I'm trying to derive the oscillator integral, os, for p to d transitions in an atom, and have come up with the expression:
  os =           (np+nd+1)!*2**(np+nd+1)*exp(p)**(np+1/2)*exp(d)**(nd+1/2)
               sqrt(5)*(exp(p)+exp(d)**(np+nd+2)*sqrt( (2*np)! * (2*nd)! )
where the Slater orbital principal quantum numbers are "np" and "nd", and the exponents are "p" and "d".
Can anyone confirm or dispute this expression, please. Evidence either way would be appreciated.
My concern is that the integral becomes very large for large values of "np" and "nd".