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Mar
30
revised $(\delta,\varepsilon)$ Proof of Limit
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Mar
30
revised $(\delta,\varepsilon)$ Proof of Limit
added 523 characters in body
Mar
30
revised $(\delta,\varepsilon)$ Proof of Limit
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Mar
30
answered $(\delta,\varepsilon)$ Proof of Limit
Mar
27
comment What does $O\left(\frac{1}{\log\log T}\right)$ mean?
Thanks. That's what I thought. So basically what the paper says is that as $T\to\infty$ the number of zeros outside the region is some constant multiple of $1/(\log\log T)$ ?
Mar
26
revised What does $O\left(\frac{1}{\log\log T}\right)$ mean?
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Mar
26
asked What does $O\left(\frac{1}{\log\log T}\right)$ mean?
Mar
25
revised fraction math help please
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Mar
25
comment Series with $e^{\frac{1}{n}}$
Shouldn't that be $+O(n^{-4})$ in your equality?
Mar
25
comment Series with $e^{\frac{1}{n}}$
You could first try expanding $e^{1/n}$ to some order ($O(1/n^k)$). Presumably the value of $k$ will be related to the existence of $1/(2n^2)$ in your summand. Then simplify if possible, and see what happens from there. Haven't tried it so can't be 100% sure, but that's what I'd do first.
Mar
24
comment Complex integration confusion
Try $z=e^{i\theta}$, where $\theta\in[0,2\pi]$.
Mar
21
comment Why Does $ \sum\limits_{k=0}^n \begin{pmatrix} n+1 \\ k+1 \end{pmatrix} p^{k+1} (1-p)^{n-k} $ sum to $ (1-(1-p)^{n+1}) $?
The binomial theorem states that: $$(a+b)^n=\sum_{k=0}^n{n\choose k}a^kb^{n-k}.$$
Mar
19
comment Having trouble understanding generalized complex numbers
@ Vim yes, that's exactly the problem I was thinking might arise.
Mar
19
comment Having trouble understanding generalized complex numbers
@ Vim yes, as I said I'm not too sure about that part as I haven't looked into it a great deal. I think if the discriminant is negative then you still have a linear equation so you could still solve for $i$. My worry was that the $i$ resulting from the $\sqrt{\cdot}$ was a "different" $i$ from that being defined. But as I say I haven't looked into this in any depth whatsoever!
Mar
19
comment Having trouble understanding generalized complex numbers
Just a thought (and might not be applicable here), regarding (1) could you not use the quadratic formula to obtain a "non-recursive" definition, e.g. $$i=\frac{q\pm\sqrt{q^2-4p}}{2}.$$ You would probably need $q^2-4p\geq 0$, although I'm not too sure about that...
Mar
18
revised On norms for “more complicated objects”
deleted 8 characters in body; edited title
Mar
17
asked On norms for “more complicated objects”
Mar
17
comment Any way to simplify integral of Confluent Hypergeometric Function of the First Kind?
@NathanMcKenzie out of interest, from what problem does this integral arise?
Mar
17
comment Any way to simplify integral of Confluent Hypergeometric Function of the First Kind?
You may have better luck using the change of variable $y=\frac{\log n}{t}+1$. This gives $dt=\frac{\log(n)dy}{y^2}$ and $t=-\log n\implies y=0$, $t=0\implies y=\infty$. Then the integral becomes: $$-z\log(n)\int_0^\infty \frac{e^{\frac{\log (n)(1-s)}{y-1}}}{(y-1)^2} {}_1F_1\left(1-z,2,\frac{\log n}{y-1}\right)dy.$$ There are plenty of tables of integrals with limits over $\mathbb{R}^+$. See e.g. Gradshteyn and Ryzhik, p.814.
Mar
11
revised Is there a name for an object with both position and velocity?
edited tags