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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