Reputation
Next tag badge:
112/100 score
19/20 answers
Badges
5 94 223
Newest
 Nice Answer
Impact
~1.7m people reached

Jul
14
comment Analytic continuation of primality function
(Sorry, it got too long for a comment…)
Jul
14
comment Find the roots of this 6th degree polynomial
So, you take all three cube roots of $-8$, twice.
Jul
14
comment Analytic continuation of primality function
Without any other restrictions, @Michael, an analytic continuation is not in general unique. Consider the gamma function: you need the additional machinery of Bohr-Mollerup just to have uniqueness.
Jul
14
answered Analytic continuation of primality function
Jul
14
comment Analytic continuation of primality function
It's possible, @Michael, but why exactly do you need a continuation? What do you actually want to do?
Jul
13
awarded  Popular Question
Jul
12
awarded  Popular Question
Jul
12
revised Cute Determinant Question
deleted 4 characters in body
Jul
12
comment Are all mathematicians human calculators?
I sometimes like doing math on paper, but I am thankful for the computer, as it lets me make mistakes much faster. ;)
Jul
11
revised Why do siamese magic squares have real eigenvalues, symmetric around zero?
added 578 characters in body
Jul
11
comment Alternating sum of product of Fibonacci numbers
What happens if you use Binet?
Jul
11
comment Change of radix without using radix 10
@Potato, I'm seeing how people can get confused; they think that the arithmetic with all the carrying and borrowing has to be done in decimal base when the same concepts exactly carry over to other bases.
Jul
11
comment Cosh and Sinh analogs
In effect, we are taking a discrete Fourier transform here.
Jul
11
revised Optimize multi-step calculation into one step?
edited tags
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 $p$.