196,852 reputation
17139311
bio website
location
age
visits member for 3 years, 11 months
seen 2 hours ago

As somebody used to say:

Does research. Smokes. Battles administration. Smokes. Wishes he could stop battling administration so that he could have more time to do research. Smokes some more.

The same. Except I do not smoke.


How to ask a good question?

This paragraph is for my personal use but freely available:

Welcome to Math.SE! Please, consider updating your question to include what you have tried and where you are getting stuck. That way, people on this site will know exactly what help you need.


Dec
19
comment Radius of convergence, prove that $\sum\limits_{n=0}^{\infty} a_n z^n$ converges absolutely for every $z \in \mathbb{C}$ with $|z| < R$
No \displaystyle in titles, please.
Dec
19
revised Radius of convergence, prove that $\sum\limits_{n=0}^{\infty} a_n z^n$ converges absolutely for every $z \in \mathbb{C}$ with $|z| < R$
edited title; edited tags
Dec
19
revised Show that $\int_0^r \frac{\mathrm{d}t}{\sqrt{r^2 - t^2}} $ is independent of $r$
rolled back to a previous revision
Dec
19
comment Show that $\int_0^r \frac{\mathrm{d}t}{\sqrt{r^2 - t^2}} $ is independent of $r$
Please avoid follow-ups after an answer was posted (and even, accepted...).
Dec
19
comment How to calculate convolution of function defining a measure
You are missing that F(r-t)=0 when t > r hence the third integral is actually on (0,r), not on (0,oo).
Dec
19
comment What is $\Gamma(1+\Gamma(1+\Gamma(1+\dots)))$?
To complete the previous comment, there are exactly two solutions (in the nonnegative real line) of $L=\Gamma(1+L)$, namely $L=1$ and $L=2$, and $x_n\to1$ for every $x_0$ in $[0,2)$, $x_n\to2$ if $x_0=2$, and $x_n\to\infty$ for every $x_0$ in $(2,\infty)$. (One says that $L=1$ is an attractive fixed point while $L=2$ is a repulsive fixed point.)
Dec
19
revised how $\prod\limits_{i=1}^{n} (2k-1)/2= (2n)!/{(4^n)n!} = (2n-1)!/[{2^{2n-1}}(n-1)!]$?
added 7 characters in body; edited tags
Dec
19
comment How to calculate the series?
There are simpler ways (see the first line of my answer).
Dec
19
comment How to calculate the series?
Now you seem to use $t^n-1\geqslant t^{n/2}$ for every $t\gt1$. Is that so?
Dec
19
revised How to calculate the series?
added 80 characters in body
Dec
19
comment How to calculate the series?
@ZubinMukerjee Yes.
Dec
19
comment How to calculate the series?
@Roger209 Right, somehow the $(-1)^n$ had escaped me. Sorry about this. See revised version.
Dec
19
revised How to calculate the series?
added 662 characters in body
Dec
19
comment How to integrate a fraction of the type $\frac{1}{(ax+b)^c(dx+e)^f}$?
((Comment by @JJacquelin now deleted.))
Dec
19
comment How to integrate a fraction of the type $\frac{1}{(ax+b)^c(dx+e)^f}$?
@JJacquelin Prestige has nothing to do with it, the important fact is that the systematization work Darwin and others did, is not done with special functions (probably for good reasons), a fact which leads to the difference between insight and naming that DavidH mentioned. Oddly, you refuse this conclusion although you were led to state it clearly in your tract.
Dec
19
comment How to calculate the series?
@ZubinMukerjee Sorry, I somehow forgot to include the link I had in mind. Done now. Thanks.
Dec
19
revised How to calculate the series?
added 48 characters in body
Dec
19
comment Constructing a joint distribution given $P(X\in A \mid Y)_\omega$
These are dangerous notations, which are rightfully avoided in every modern textbook on the subject that I know. Billingsley probably means $P((X,Y)\in J\mid X)=Q(X)$ where $Q(x)=P((x,Y)\in J)$ for every $x$ (an identity which is only true if $Y$ is independent of $X$, by the way), and this expanded formulation is much preferable.
Dec
19
comment How to integrate a fraction of the type $\frac{1}{(ax+b)^c(dx+e)^f}$?
@JJacquelin Interestingly, your tract, probably meant as a defense of special functions, nearly finishes with: "Pour aider à y voir plus clair dans tout ce bestiaire de fonctions, il faudrait songer à embaucher quelques naturalistes afin d'y mettre une certaine systématique. On attend les Jussieu, Darwin, Henning... des mathématiques." ...which (in the absence of the Jussieus, Darwins, etc., of this special field of mathematics) is exactly what DavidH's comment is pointing at.
Dec
19
comment How to calculate the series?
Alternating? $ $