# Absane

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Absane is a member of SciForums and one of three moderators of Free Thoughts.

• Absane drinks Athelwulf's pee.
• nobody pays attention to Absane.
• nobody likes absane because he is a camper.

He's as interesting as a math major, and has about as much depth as a vector of order one. If he was a matrix, he'd have only trivial solutions. He likes his truck a lot, even though its rusting to pieces.

## Favorite Equations

• $F = \frac{dp}{dt}$
• $i^i = e^{-\pi/2}$
• $\gamma = \lim_{n \rightarrow \infty } \left( \left( \sum_{k=1}^n \frac{1}{k} \right) - \ln (n) \right)=\int_1^\infty\left({1\over\lfloor x\rfloor}-{1\over x}\right)\,dx$
• Collatz Conjecture:

$f(n) = \begin{cases} n/2 &\mbox{if } n \equiv 0 \\ 3n+1 & \mbox{if } n\equiv 1 \end{cases} \pmod{2}.$

$a_i = \begin{cases}n & \mbox{for } i = 0 \\ f(a_{i-1}) & \mbox{for } i > 0\end{cases}$

$\forall n \in \mathbb{N} > 0 \ \exists i \in \mathbb{N}: (a_0 = n \Rightarrow a_i = 1)$

• $\lim_{n \rightarrow \infty } \left( \sum_{k=1}^n \frac{1}{k^r} \right) = \lim_{n \rightarrow \infty } \left( \prod_{p \in P_n} \frac{1}{1-\frac{1}{p^r}} \right), P_n = \{x|x \, \mbox{prime}, x \leq n\}$

## Independent Research

Some odd time ago, Absane derived an equation very close to the Ramanujan expansion for the harmonic series $1 + \frac{1}{2}+ \frac{1}{3}+ ... + \frac{1}{n-1}+ \frac{1}{n}$

• $H_{n} \sim ln(\sqrt{n^{2} + n}) + \gamma$

He showed it to his mum, and got a cookie.