Expansion of $b^{(x+a)^{-n}}$ where $0 \le b \le 1$

27 Views Asked by At

The expansion of the negative binomial series is given below.

$$ (x+a)^{-n} = \sum^\infty_{k=0} (-1)^k \begin{pmatrix}n + k - 1\\k\end{pmatrix} x^ka^{-n-k} $$ when $|x| < a$.

What would be the expansion of $b^{(x+a)^{-n}}$ where $0 \le b \le 1$?