# Tagged Questions

461 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 ...
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### 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 ...
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### 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 $k$, ...
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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 ...
### Why is $\frac{\pi^2}{12}=ln(2)$ not true ?
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 ...