# Tagged Questions

Questions on Bernoulli numbers, a special sequence of rational numbers that arise as the coefficients in the power series expansions of certain elementary functions.

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### Singularities of $z\mapsto\frac{z}{\mathrm e^z-1}$ and the Bernoulli numbers of its expansion

Characterize all singularities of $$z\mapsto\frac{z}{\mathrm e^z-1}.$$ What is the radius of convergence of the taylor expansion of $$\frac{z}{\mathrm e^z-1}=\sum_{n=0}^\infty B_n\frac{z^n}{n!}$$ ...
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### What are Bernoulli numbers? Is there any identity to find these numbers?

What are Bernoulli numbers? Is there any particular pattern to find these numbers like the Fibonacci numbers? How are they applicable in Taylor expansions of hyperbolic tangents?
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### solving limit from 2nd bernoulli number

I'm having trouble solving the following limit: $$\lim_{x \to 0}\frac{xe^{2x}+xe^{x}-2e^{2x}+2e^{x}}{(e^{x}-1)^{3}}$$ substitution gives a 0/0 indeterminate, and we can get around it with de l'...
In order to generate $M$ paths of length $N$ I have to generate Bernoulli variables. In Matlab I used: Q=binornd(1,lambda,L,N); Now I want to generate this for a sequence of values lf lambda, but I ...