J. M.
Reputation
49,288
409/400 score
 1d awarded Nice Answer 1d revised Is there any proof that the Riemann Zeta function is not elementary? edited tags 2d comment Why does this matrix give the derivative of a function? In fact, this is sometimes taken to be the definition of a matrix function when evaluated at a Jordan block; see this. See this paper as well. Nov 21 revised The approximation of first-ordered modified Bessel function of the second kind edited tags Nov 19 revised Why does the google calculator give tan 90 degrees = 1.6331779e+16? edited tags Nov 16 comment proof: inverse of lower triangular identity matrix Your observation only works for so-called "Gauss transforms", which are rank-1 corrections to the identity matrix that turn up in LU decomposition. Golub and Van Loan should have a proof of this. Nov 14 awarded Enlightened Nov 14 awarded Nice Answer Nov 13 awarded Revival Nov 13 revised Associated Legendre polynomials of fractional order added 4 characters in body Nov 9 revised What is Cauchy Schwarz in 8th grade terms? added 2 characters in body Nov 9 comment Explaining to a kid why a negative × negative = positive? Really, it's never not easy to explain why multiplying two negatives makes a positive. Your kid shouldn't be not fine with it. Nov 8 comment Does the phrase “If you don't use it, you lose it” apply to mathematics? Not having a very good memory, I still forget things even if only a short span of time has passed since the last time I used it. However, I compensate by trying to at least remember where to look things up (i.e. references) whenever I need them. But yes, practice is key, as previously mentioned. Nov 7 revised pdfs of i.i.d. with uniform distribution deleted 1 character in body Nov 6 comment Can any 3d rotation be done with only two angles? Here's a different way of looking at it: recall that any 3D rotation matrix has an axis-angle representation (one angle). But, this axis is not necessarily aligned to the coordinate axes! So, you need one rotation to take the axis to a coordinate plane (two angles), and another one to have it coincide with a coordinate axis (three angles). Nov 4 comment What kind of distribution is this (PDF bounded within interval)? For reference: the PDF presented here can be seen as a suitably scaled quadratic B-spline basis function. Nov 4 comment pdfs of i.i.d. with uniform distribution Well, looking at the convolution-based recursive definition, I suddenly recalled that one way to start B-spline theory is to consider them as repeated convolutions of a boxcar function. Here are two references, among others. Nov 4 comment pdfs of i.i.d. with uniform distribution For comparison purposes: BSplineBasis[n - 1, x/n] // PiecewiseExpand // Simplify. It's amusing how a function from a distant field can represent the solution... Nov 3 accepted A golden ratio series from a comic book Nov 2 awarded Good Answer