J. M.
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 Apr 25 comment Construct certain univariate functions over bounded interval having given set of moments This seems more like a math question than a Mathematica question. Apr 24 comment Are we allowed to compare infinities? The drawing should sell it, hopefully. :) Apr 24 comment Are we allowed to compare infinities? ...with attribution, of course. Apr 24 comment Why is Euler's number used as a base for logarithms? Your last formula is exactly what was being said in your quote, but couched in admittedly very high-level language. Apr 23 comment Why is Euler's number used as a base for logarithms? "Isn't it much simpler to use 10 as a base?" - it depends on the application, of course. For things like pH and other p-values, of course the common logarithm is the convenient one. For calculus, due to the property peter mentioned (among many other things), $e$ is the "nice" base. Apr 22 comment Showing that a matrix is symmetric positive definite You can easily reformulate the route here in terms of LU; the only important facts are that SPD matrices do not need pivoting, and there is a relationship between LU and both Cholesky and $\mathbf L\mathbf D\mathbf L^\top$. Apr 22 comment Showing that a matrix is symmetric positive definite …and you never covered Schur complements either? Apr 20 comment What equation produces this curve? Certainly, the basis changes between the Hermite and Bézier systems are well-known to those who know them. :) In any case, sigmoids such as the OP's are very cheaply constructed as appropriate interpolating polynomials with prescribed derivatives, and your procedure is the most straightforward way to go about it. As another aside: computer graphics buffs may be more familiar with this as (an appropriate rescaling of) the smoothstep() function. Apr 20 comment What equation produces this curve? For searching purposes: what was constructed here is a cubic Hermite interpolating polynomial. Usually does a nice job if the derivative values are sanely chosen. Apr 13 comment Is basis change ever useful in practical linear algebra? Not just for powers; in fact, this can be used anytime one wants to evaluate a function with matrix arguments, like the exponential or the sine. In the nondiagonalizable case, one has to be content with the Jordan form. Apr 10 comment Is the catenary the trajectory of anything? @Oscar, yes, the Hall/Wagon paper also addresses the infinite-sides case, too. :) Apr 10 comment Improper integral involving sinc function and Pochhammer symbol A few manipulations give the equivalent integral $$\int_{-\infty}^\infty \frac{\Gamma(1+n)}{\Gamma(1+t)\Gamma(1-t+n)}\mathrm dt=\int_{-\infty}^\infty \binom{n}{t}\mathrm dt$$ Apr 10 comment What's problematic about finding out if a large number is Prime or not? It is hard to check for a large number's primality, yes, but at least that is a comparatively easier task than attempting to factor a large number. (As an aside, most of the efficient probabilistic tests should be properly called "compositeness tests", since they can show compositeness with certainty, but not primality.) Apr 10 comment Function that maps the “pureness” of a rational number? Put another way, your "another possibility" is just the ratio of the LCM to the GCD. Apr 10 comment Computing Bezier curve of a high order ...depends on the configuration of the ten points of course. OP unfortunately did not show even a picture. Apr 10 comment Why are there so many primes in the convergents of Pi? ...and of course, the convergents thus produced will always be in lowest terms. Apr 10 comment In a right triangle, can $a+b=c?$ Since nobody apparently brought it up: look up the triangle inequality. Apr 7 comment Is the catenary the trajectory of anything? Then you'll want to see Stan Wagon actually riding his square-wheeled bicycle. ;) Apr 7 comment Is the catenary the trajectory of anything? That's certainly your choice to make, but then "trajectory" does not mean what you imply it means. Apr 7 comment Is the catenary the trajectory of anything? Wagon and Hall, in their paper, show that a straight line "wheel" can "roll" (in a sense defined in the paper) on a catenary "road"; the polygonal case is a slight modification of this. Have a look at their paper if you're interested. Nevertheless, I do not think it is an answer to the question, as the catenary is not really the locus here.