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**62**

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### Roots of truncations of e^x - 1

During a talk I was at today, the speaker mentioned that if you truncate the Taylor series for $e^x - 1$, you'll get lots of roots with nonzero real part, even though the full Taylor series only has ...

**17**

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**2**answers

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### Integral representation of higher order derivatives

I'm quite curious about the following phenomena, that still puzzle me although I have a proof, and I'd be really glad if someone may shred some light, showing an interpretation or a generalization. I ...

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**2**answers

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### power series of the reciprocal… does a recursive formula exist for the coefficients. [closed]

Hello
If $f(x)=\sum _{n=0}^{\infty } b_nx^n$, and $\frac{1}{f(x)}=\sum _{n=0}^{\infty } d_nx^n$. Then the coefficients of the reprical of f can be written down. The first few terms are:
$d_0 = ...

**3**

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**1**answer

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### Approximate the square root of (1-X) efficiently through (nested) products

Currently, I encountered a problem of approximating the following
series:
$$
(I-X)^{-\frac{1}{2}}=I+\frac{1}{2}X+\frac{1\cdot3}{2\cdot4}X^{2}+\frac{1\cdot3\cdot5}{2\cdot4\cdot6}X^{3}+\ldots
$$
where ...