4,802 reputation
918
bio website motls.blogspot.com
location Czech Republic
age 41
visits member for 3 years, 7 months
seen Dec 9 at 8:39

Hi, I am a string theorist and a publicist.


Dec
9
awarded  Caucus
Sep
30
awarded  Explainer
Aug
9
comment Plis, What is the orthogonality conditions for associated legendre polynomials with both two different indexes
If some indices are equal, the results are mathworld.wolfram.com/AssociatedLegendrePolynomial.html
Aug
2
comment Why does $1+2+3+\dots = -\frac{1}{12}$?
Dear @AxelBoldt, $0+1+2+3+4+\dots $ is also demonstrably and always equal to $-1/12$, and it may be shown by pretty much the same proof. And $1+1=2$. If all entries except for a finite number are zero, then one adds a finite number of terms which always has uncontroversial rules.
May
7
awarded  Yearling
Mar
6
comment Why does $1+2+3+\dots = -\frac{1}{12}$?
Sure, it's a completely analogous sum. Just like $1+2+3+\dots$ quantifies the ground state energy in 1+1 dimensions (of a string), $1+1+1+\dots$ quantifies the ground state's charge (of a system of free fermions, for example). It's really the reason why the two degenerate states $|0\rangle$ and $c_0|0\rangle$ have ghost numbers $\pm 1/2$, for example.
Feb
10
comment Why does $1+2+3+\dots = -\frac{1}{12}$?
It might be but it is a wrong conclusion. The key property of this $\infty$, which may be subtracted by a counterterm, is that it is independent of all independent variables, so it is formally a scale-invariant constant, and $0$ is the number to be associated with it. The fact that the sum of integers equals $-1/12$ is perhaps the most important fact about mathematics among the laymen - and among mathematicians without breadth and depth.
Feb
8
answered Equivalence of Two Lorentz Groups
Jan
24
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Dear @Pedro, I am saying that $\zeta(2k+1)$ are transcendental numbers because I am ready to bet all my wealth on the validity of the claim. After all, even $\pi^n$ are transcendental numbers for rational nonzero values of $n$ so even zeta of even positive integers are (provably) transcendental. But the zetas of odd positive integers are (I claim without a rigorous proof) much more transcendental than the powers of $\pi$. I never claimed that I had a rigorous proof of the transcendentality but if you want to claim that I said something incorrect, you should have a proof which you don't have.
Jan
24
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Nope, it's just believed by me and almost everyone that they're transcendental. The much "easier" proof that zeta(3) is irrational came just recently, in 1978, see en.wikipedia.org/wiki/Ap%C3%A9ry's_theorem
Jan
23
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Nice, +1. An alternative calculation of $\zeta(0)=-1/2$ appears early in this article: motls.blogspot.com/2014/01/… - See my comment under the OP's question for 4 more articles about the topic if you wish...
Jan
23
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Five more articles with 8 different ways to compute the sum of integers (most of the methods extend to the "sum of ones", too) etc.: motls.blogspot.com/2007/09/… motls.blogspot.com/2011/07/… motls.blogspot.com/2014/01/… motls.blogspot.com/2014/01/… motls.blogspot.com/2014/01/…
Jan
11
comment Why does $1+2+3+\dots = -\frac{1}{12}$?
"Incorrect", "not right", and "opposite of right" are the same thing, also known as "synonyma".
Sep
20
comment The inverse Fourier transform of $1$ is Dirac's Delta
Well, I think you would also have to discuss that the negative regions of $(\sin x)/x$ don't combine to other distributions like $\delta'$ etc. But otherwise OK, I upvote it.
Jun
25
comment Fourier transform of a signal sequence?
I would be sort of surprised if there is an analytic formula for the Fourier transform of this contrived function.
Jun
18
awarded  Good Answer
May
29
revised How find the number of $z$,such that$ |a^2-b^2-b+1|\le 10$
added 365 characters in body
May
29
answered How find the number of $z$,such that$ |a^2-b^2-b+1|\le 10$
May
28
answered Evaluate integral in terms of Gamma function
May
24
revised Grover Algorithm Orthogonal vectors
added 15 characters in body