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seen Jul 21 at 17:43

Apr
8
comment Rules of Division
@Bill - An answer is an answer. If original content was the requirement, most answers would be illegitimate because in most cases people would be quoting from, or regurgitating material from another source -- often without credit given.
Apr
8
comment Rules of Division
+1, I was tempted to down-vote because the motivation behind stackexchange-like sites -- at least, based on the FAQs I've read -- is to become something like Wikipedia, but designed in such a way to motivate people to more proactively contribute content. Wikipedia doesn't just contain external links, they actually provide content. If the link was to some message forum or some other site that didn't have a high likelihood of long-term survival, I probably would've down-voted.
Apr
6
comment $\ln(x^2)$ vs $2\ln x$
@Americo - That's only true for real $x$. $(a + b i)^2 = a^2 + a b i - b^2$, whereas $|a + b i|^2 = \sqrt{(a + b i)(a - b i)}^2 = \sqrt{a^2 + b^2}^2 = a^2 + b^2$. The two are not the same.
Apr
5
comment Relation between complex Jacobian and differential of a complex number
I don't see the question. J is a gradient operator, and it appears the author is stating (not claiming or ignoring a proof for) that the jacobian matrix is $J\{e^{i \phi(u,v)}\} = f'(u + iv)$ -- which is a matrix of 1st derivatives w/respect to each variable. The ambiguity I see is in the definition of $f'(.)$; is it the derivative with respect to the single complex variable $z = u + i v$?
Apr
1
comment Help with summing a power series
@Mitch - ${-n \choose k} = (-1)^{k}{{k - (n + 1)} \choose k}$, for positive $n$. The $(-1)^{k}$ coefficient keeps the value of the quantity positive (provided $n > k$?). Ignoring sign, this is the number of ways to arrange $|k - (n + 1)|$ items taken $k$ at a time. The $\frac{1}{2}$ I don't have a great intuitive description for, sorry.
Apr
1
comment Help with summing a power series
@Mitch - The negative value is talked about in the wikipedia link I'm about to link to. The non-integer values could be covered by the interpretation $n! = \Gamma(n+1)$ -- though I'll confess, I don't know if there are any technicalities I'm missing with that blanket statement about non-integer $n$. Wikipedia link to binomial coefficients: en.wikipedia.org/wiki/…
Apr
1
comment Help with summing a power series
@Mitch - I suppose that's one interpretation. I see the stackexchange-style sites as a far more global resource. While the answer may only serve the OP by doing his homework for him, this isn't an IRC chat-room or newsgroup post where a small audience will get something out of the response.
Apr
1
comment Help with summing a power series
@Mitch - If you don't like the question, downvote it. If you think the answer given is badly written or contains errors, downvote it. But this is just not classy.
Apr
1
comment Help with summing a power series
It looks like answers are being downvoted as well for, it would seem, no good reason. If you think the questioner is being lazy, fine, but downvoting an answer because you don't think the question deserves an answer is extremely rude. If you downvote, at least provide a reasonable critique.
Mar
28
comment General Introduction to Functional and other Mathematic Notations
@Garet - Older math textbooks (particularly if they're aimed at juniors/seniors/grad students) are more in-line with what you'd see in an RFC. They're often very short books (eg, I have a book on complex analysis that's about 70 pages long, but it covers most of the material you'd see in a typical complex analysis class). I'm not overly fond of the style. As with programming books, I like to see a lot of examples. But, that might not be a bad place to look if that's what you want.
Mar
26
comment General Introduction to Functional and other Mathematic Notations
@Myself: That was a response to you, not him.
Mar
26
comment General Introduction to Functional and other Mathematic Notations
Yikes. No more late-night posting for me. I deleted the first two because they had nothing to do with responding to your comment.
Mar
26
comment General Introduction to Functional and other Mathematic Notations
or string the ideas together into a coherent and correct proof.
Mar
26
comment General Introduction to Functional and other Mathematic Notations
My point is it isn't just some set of axioms and rules. It IS a language with a logical flow or rhythm. If sentence words threw I order any did, I together a in then the sentence wouldn't be readable to you. The same thing is true in math. Just because you know the words and symbols doesn't mean you know how to string them together in a manner that is readable.
Mar
22
comment The phrase “coordinate-wise” and its meaning
So, another potential interpretation of that, it sounds like, is you can apply a function $f: \Re^1 \mapsto \Re^1$ coordinate-wise to a matrix or array by applying it element-wise.
Mar
22
comment The phrase “coordinate-wise” and its meaning
Ah. I see your point. So, if for example I have a scalar function $\sigma$ I want to apply to the elements of a vector/matrix (eg, $\mathbf{Y} = \mathbf{\sigma}(\mathbf{X})$ ), I could say $\mathbf{\sigma}$ is evaluated "coordinate-wise" on elements of $\mathbf{x}$. You should write up your response as an answer so I can accept it.