robjohn

West Hills, CA

none

Age: 55

the mean square The Mean Square
(with one standard deviation and several unusual ones)

aka Rob Johnson

$\LaTeX$ support for Chat

9m
answered process of showing that a number is irrational
1h
revised Sum over all non-evil numbers
the log estimate was not correct, but we get the same final estimate from a far simpler consideration
1h
answered Sum over all non-evil numbers
15h
comment Ellipse focus locus
How is the ellipse rolling on a circle? is the ellipse on the inside or outside? is the circle rolling and the ellipse on top? More information is needed, I think.
16h
answered Probability of caugh at least 1 of one type of fish
19h
comment Challenging Infinite summation involving the zeta function
@DivyanshGarg: While your question is a duplicate, seeing it lead me to the other question, to which I have added an answer. I hope that satisfies some of your desire to see other answers. (+1)
20h
answered Polygamma function series: $\displaystyle\sum_{k=1}^{\infty }\left(\Psi^{(1)}(k)\right)^2$
2d
revised Some of my answers downvoted unnecessarily?
adjust to mention the answer tooltip
2d
answered Some of my answers downvoted unnecessarily?
Aug
27
answered Integral of $\ln(x)\operatorname{sech}(x)$
Aug
26
answered Formulating a recursive definition
Aug
26
comment Finding the Moment Generating function of a Binomial Distribution
You are missing an $e^{tx}$ in the first line.
Aug
26
answered Finding the Moment Generating function of a Binomial Distribution
Aug
26
comment Evaluate$ \int_0^{\frac{\pi}{2}} \ln(1+\cos x) dx$
The simplest method seems to be to use an identity that I've used quite a bit: $$\log(1+\cos(x))=2\sum_{k=1}^\infty(-1)^{k-1}\frac{\cos(kx)}{k}-\log(2)$$ Integrating this and knowing Catalan's Constant finishes things up. I use these in my answer.
Aug
26
awarded Necromancer
Aug
26
comment $\sum_{n=1}^{\infty}\frac{H_n}{n^2 2^n}=\zeta(3)-\frac{1}{2}\log(2)\zeta(2)$
I forgot that you had used the generating function of the Harmonic Numbers here. I used its integral for the sum of $H_n^2/n^2$ recently.
Aug
26
answered Evaluate$ \int_0^{\frac{\pi}{2}} \ln(1+\cos x) dx$
Aug
26
comment How to solve $e^x=x$?
@JackD'Aurizio: do you have any estimates from the integral of how many roots there are inside a given region (circle, square, whatever)?
Aug
26
comment How to solve $e^x=x$?
@XiangruLian: This formula works if the roots are all simple. Multiple roots are counted with their multiplicity.
Aug
26
answered How to solve $e^x=x$?
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