What is the Taylor expansion of $ $ \prod_{i=1}^n\frac{1}{\sqrt{1-x_i}}$ $ around $ (0,0,…,0)$ ？I know that we can write it as $ $ \prod_{i=1}^n\left(1+\sum_{k=1}^{\infty}\frac{(2k-1)!!x_i^k}{(2k)!!}\right)$ $ But how to simplify it?

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# Tag: $\prod_{i=1}^n1x_i^{1/2}$

## Taylor expansion of $\prod_{i=1}^n(1-x_i)^{-1/2}$ around 0

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What is the Taylor expansion of $ $ \prod_{i=1}^n\frac{1}{\sqrt{1-x_i}}$ $ around $ (0,0,…,0)$ ？I know that we can write it as $ $ \prod_{i=1}^n\left(1+\sum_{k=1}^{\infty}\frac{(2k-1)!!x_i^k}{(2k)!!}\right)$ $ But how to simplify it?

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