# Tagged Questions

**5**

votes

**3**answers

426 views

### Taylor series coefficients

This question arose in connection with A hard integral identity on MATH.SE.
Let
$$f(x)=\arctan{\left (\frac{S(x)}{\pi+S(x)}\right)}$$
with $S(x)=\operatorname{arctanh} x -\arctan x$, and let
...

**6**

votes

**1**answer

180 views

### Laurent expansion of inverse of vandermonde determinant

I wish to find the coefficients of the Laurent expansion of the inverse of the Vandermonde determinant, that is, the Laurent expansion at 0 of
$$\prod_{1\leq i<j \leq n}(x_j-x_i)^{-1}.$$
We can ...

**1**

vote

**1**answer

89 views

### Estimate the scale of the power series with Poisson pdf/pmf-like terms

I would like to have an estimate for the series
$$P(t) = \sum\limits_{k = 0}^\infty (e^{-t}\frac{t^k}{k!})^m,$$
where $e$ is the base of natural logarithm, $k!$ is the factorial of the integer $k$, ...

**18**

votes

**2**answers

1k views

### 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 ...

**13**

votes

**3**answers

3k views

### Why is $ \frac{\pi^2}{12}=ln(2)$ not true ?

This question may sound ridiculous at first sight, but let me please show you all how I arrived at the afore mentioned 'identity'.
Let us begin with (one of the many) equalities established by Euler:
...

**7**

votes

**2**answers

2k views

### Estimate for tail of power series of exponential function?

I would like to have an estimate for the infinite series
$$
\sum_{k=B}^\infty \frac{A^k}{k!},
$$
where $A$ is a large positive quantity and $B$ is just a little bit bigger than $A$, namely, $B = A + C ...