# All Questions

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### General term of sequence 3

Let be $$6,8,12,15,20,24,30,35,42,…$$ a sequence of natural numbers. Guessing the recurrence then using generating functions I can prove that general term of sequence is ...
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### How to prove cardinality equality ($\mathfrak c^\mathfrak c=2^\mathfrak c$)

How do I prove this cardinality equality:$\mathfrak c^\mathfrak c=2^\mathfrak c$ I have failed to prove this after lots of trail - but I am certain it's true How can I prove this?
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### Wikipedia Article — Legendre Transform

I was reading the wiki article on Legendre Transform. I would be grateful if someone could explain the section at http://en.wikipedia.org/wiki/Legendre_transformation#Examples ie how they arrived at ...
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### Finding a primitive explicitly

Let $A=\{z\in\mathbb{C}~:~|z|>4\}$. Let $f(z)=\frac{z}{(z-1)(z-2)(z-3)}$ and $g(z)=\frac{z^2}{(z-1)(z-2)(z-3)}$. I have been asked whether or not $f$ and $g$ have global primitives in $A$ and if ...
I want to know the idea/intuition behind the Dirichlet integral. For example consider $$I(\alpha) = \int_0^{\delta} g(t) \frac{\sin(\alpha t)}{t} dt$$ . Why would $I(\alpha)$ tend to some constant ...