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Mar
5
awarded  Nice Answer
Mar
5
revised A little integration paradox
added 76 characters in body
Mar
5
comment Anti-derivative of continuous function $\frac{1}{2+\sin x}$
Possible duplicate of A little integration paradox
Mar
4
comment Why does the Cauchy-Schwarz Inequality even have a name?
@Lucian, that should be "After proof, each theorem...", methinks. ;)
Mar
3
comment Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?
Yes, this is still considered a continued fraction; in general they can have complex partial numerators and partial denominators. Simple continued fractions are the ones whose partial numerators are all $1$.
Mar
3
comment Why does the Cauchy-Schwarz Inequality even have a name?
In addition to that: any result that just keeps popping up in different contexts deserves to have a name attached to it.
Feb
29
revised Good “history of mathematical ideas” book?
edited body
Feb
26
revised Functions that are their Own nth Derivatives for Real n
added 143 characters in body
Feb
24
revised By Changing My Option, How Does This Double My Chance of Winning?
edited tags
Feb
24
comment By Changing My Option, How Does This Double My Chance of Winning?
Look up Monty Hall.
Feb
23
revised $\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?
added 307 characters in body
Feb
23
comment Complex integral: how to parameterise a circle?
You might be more familiar with the parametrization $x=h+r\cos t,\quad y=k+r\sin t$ of a circle. To use it in a contour integral, put those two components together as $z=x+iy$; this gets you $z=(h+ik)+r\exp(it)$.
Feb
22
awarded  Nice Answer
Feb
21
comment Recursive function including Bessel functions
Did you mean to post this on the Mathematics site? This site is for the users of the software Mathematica.
Feb
21
comment Find eigen values of a block-diagonal matrix
What is $(n-2p)+p$?
Feb
20
comment Can you justify the existence of a $x_{*}$ solving $\mbox{li}(x_{*})=\mbox{erf}(x_{*})?$
@A.S., if that is the method you choose to evaluate the error function and the logarithmic integral, then yes. Otherwise, there are more efficient methods than quadrature that can be used.
Feb
20
comment Can you justify the existence of a $x_{*}$ solving $\mbox{li}(x_{*})=\mbox{erf}(x_{*})?$
You know that you can just use Newton-Raphson for this, right?
Feb
20
comment Can you justify the existence of a $x_{*}$ solving $\mbox{li}(x_{*})=\mbox{erf}(x_{*})?$
A Cauchy principal value often just differentiates in the same way as a normal integral; you can go back to the original definition of it to see this. Actually, since in your definition, the lower limit is the Soldner-Ramanujan constant, it is not even a PV integral anymore.
Feb
20
comment What is the computational benefit of Aitken's $\Delta^2$ process?
Yes, you need to find a certain number of $x_n$. The idea behind $\Delta^2$ is that $y_n$ will often be a better approximation than $x_n$, and only $x_m$, $m \gg n$ will be of comparable accuracy. That is, you get more good digits from relatively few members of the initial sequence.
Feb
20
comment What does “Mathematics of Computation” mean?
Back in the day, the journal was called "Mathematical Tables and Other Aids to Computation" (MTAC), since the journal was concerned with methods for hand calculation. Usually this meant tables generated by computer, or descriptions of algorithms that can easily be used by "computers" (in the original sense of the word). After computers became more prominent, AMS changed the title to its current form. As might be surmised, computational methods (usually for numerical analysis or number theory) are the sort of topics this journal deals with.