J. M.
Reputation
50,198
416/400 score
 Jan 28 awarded Good Answer Jan 14 awarded Necromancer Dec 20 awarded Good Answer Dec 20 awarded Guru Dec 16 revised How many combinations are possible? edited tags Dec 13 comment I like math, but can't keep up with the pace. You will fail to get the required intuition at times, yes. But you have to try again after. Dec 13 comment I like math, but can't keep up with the pace. ...and why are you so afraid of sinking? Can you not try again after? Dec 13 comment Is there a means of finding an infinite sum by means of altering it into an integral? The other possibility is to express the sum as a contour integral, with the summand multiplied by a factor with poles at the right places. Dec 13 revised Convergence of $\sum_{k=1}^{n} f(k) - \int_{1}^{n} f(x) dx$ deleted 45 characters in body Dec 13 comment Is there a means of finding an infinite sum by means of altering it into an integral? Alternatively, look up the Abel-Plana formula. Dec 12 awarded Revival Dec 12 revised What's the area of the shape defined by all points whose distances from two focal points multiply to give the same product? deleted 5 characters in body Dec 12 comment Sum of the Stieltjes constants? (divergent summation) Then, it is possible that PARI/GP's algorithms are unable to handle this. In Mathematica, I used the double exponential quadrature method of Takahasi and Mori. Dec 12 revised Computing the Integral $\int r^2 \text{J}_0(\alpha r) \text{I}_1(\beta r)\text{d}r$ edited tags Dec 12 comment Generalization for Stirling numbers 2nd kind to negative column-indexes? So, doesn't that reflection relation answer the question in your title? Dec 12 comment What is the sum of Psi/Digamma-function of consecutive arguments? Is there a closed form? @Kirill, are you sure of all those digits you quoted? My own experiments of summation + extrapolation only seem to guarantee the first six significant digits of your result, which makes me suspicious of your other digits. Dec 12 comment Sum of the Stieltjes constants? (divergent summation) Have you tried taking the imaginary part before integrating? Dec 12 comment Generalization for Stirling numbers 2nd kind to negative column-indexes? Have you seen this? Formula 2.4 there might be of interest to you. Dec 12 comment What is the half-derivative of zeta at $s=0$ (and how to compute it)? I'll link to a previous thread of yours, where I derived expressions that will pop up in the Maclaurin series for $\zeta(s)$. Semidifferentiate this series, replace $s$ with $0$, and you now have a series to start with. I might write something up late if I find the time. Dec 12 comment What is locus of a fixed point on a circle of radius $r$ rolling over the curve $y=\sin x$? I used Mathematica to generate the cartoon, @marty.