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Jul
11
comment Estimating the value of an improper integral numerically
The variable substitution in this answer has in fact been recommended by Takahasi and Mori as an excellent way of dealing with infinite integrals, after which one can then use the trapezoidal rule. But, since the trapezoidal rule is being used anyway, the double exponential substitution might possibly give better results.
Jul
11
comment is true that $\sum_{n=0}^\infty B_n(-1)^n=\frac{\pi^2}{6}$?
@Herick, you really should have included that information in your original question. What you did is to convert a convergent improper integral into a series that is formally divergent, but regularizable.
Jul
11
comment is true that $\sum_{n=0}^\infty B_n(-1)^n=\frac{\pi^2}{6}$?
Well, you can re-express the sum as $$\frac12-2\sum_{k=0}^\infty \frac{(-1)^k (2k)! \zeta(2k)}{(2\pi)^{2k}}$$ where we used the relationship between Riemann's function and the Bernoulli numbers, and you should now see why it is divergent as it stands. But, again, maybe it can be regularized...
Jul
11
comment is true that $\sum_{n=0}^\infty B_n(-1)^n=\frac{\pi^2}{6}$?
More simply, $\frac12+\sum\limits_{n=0}^\infty B_{2n}$. Of course, you know that the actual sum is divergent, but you are asking for a particular regularization.
Jul
11
comment Looking to create a non-linear phase portrait of an “Elliptical Spiral”
"you continue to do this untill up until infinite" - so for instance, the next point is $(0, -1/4)$? Otherwise, your rule is unclear...
Jul
11
comment Change of radix without using radix 10
So, represent all your $d$'s and $b$ in radix $p$, and do all your arithmetic in base $p$.
Jul
11
comment Re-Expressing the Digamma
The poles of the digamma function, as well as its not being periodic, preclude the Fourier series expression, unless you only want to consider some interval that does not contain a pole. At best, all you have is the reflection formula involving the cotangent.
Jul
11
revised Re-Expressing the Digamma
edited tags
Jul
11
comment Why do siamese magic squares have real eigenvalues, symmetric around zero?
(Effectively, this is the same as Jyrki's answer.)
Jul
11
answered Why do siamese magic squares have real eigenvalues, symmetric around zero?
Jul
9
awarded  Popular Question
Jun
20
awarded  Enlightened
Jun
19
awarded  Nice Answer
Jun
18
comment How to get this numerical solution of a integro-differential equation
Why not help Mathematica out a bit and see if you can turn your integro-differential equation into an ODE?
Jun
13
revised How to visualize the Gaussian curvature of a 3D surface using color?
improved versions of routines
Jun
12
awarded  Notable Question
Jun
10
comment How to make Poisson voronoi diagram
The output of RandomVariate[PoissonDistribution[(* stuff *)]] is an integer, right? That is the number of points you need to generate in the cell that number is associated with.
Jun
10
comment How to make Poisson voronoi diagram
You just cut the square into $n\times n$ smaller squares, for some $n$.
Jun
10
comment How to make Poisson voronoi diagram
The idea is relatively simple: in two dimensions, if you have a square region, split it into "cells", associate each cell with a Poisson-distributed random integer (call it $k$), and generate $k$ points in that cell with the coordinates drawn from a uniform distribution.
Jun
7
awarded  Nice Answer