Reputation
7,276
Top tag
Next privilege 10,000 Rep.
Access moderator tools
Badges
10 62
Impact
~62k people reached

  • 0 posts edited
  • 0 helpful flags
  • 237 votes cast
Dec
30
comment Finding Cauchy Principal Value for $\int_0^\infty \frac{\ln^2x }{(1-x)^2\sqrt{x}(x-4)} dx$
Thanks Ron. I look forward to your "messy but systematic presentation" complex method, and I will no longer worry about 'usurpation'. :)
Dec
29
revised Evaluation of $\int \limits _0 ^{2 \pi} \frac {(r \cos \phi +x) \cos(n\phi)} {r^2+2xr \cos \phi +x^2} d\phi$
added more detail.
Dec
29
revised Evaluation of $\int \limits _0 ^{2 \pi} \frac {(r \cos \phi +x) \cos(n\phi)} {r^2+2xr \cos \phi +x^2} d\phi$
typo and addendum
Dec
29
revised Evaluation of $\int \limits _0 ^{2 \pi} \frac {(r \cos \phi +x) \cos(n\phi)} {r^2+2xr \cos \phi +x^2} d\phi$
added 103 characters in body
Dec
29
revised Evaluation of $\int \limits _0 ^{2 \pi} \frac {(r \cos \phi +x) \cos(n\phi)} {r^2+2xr \cos \phi +x^2} d\phi$
add more thoughts on the topic.
Dec
29
answered Evaluation of $\int \limits _0 ^{2 \pi} \frac {(r \cos \phi +x) \cos(n\phi)} {r^2+2xr \cos \phi +x^2} d\phi$
Dec
28
comment Finding Cauchy Principal Value for $\int_0^\infty \frac{\ln^2x }{(1-x)^2\sqrt{x}(x-4)} dx$
Hi RG. Wow, you did not get the same thing?. May I ask what you got?. I double checked and keep getting the same solution. But, not matching with you get makes me worry I done something wrong somewhere; which is probably more likely than you. I just noticed that Lucian posted a comment matching my answer. It was under a link that said, "3 more comments" and I hadn't noticed it at first.
Dec
25
answered Finding Cauchy Principal Value for $\int_0^\infty \frac{\ln^2x }{(1-x)^2\sqrt{x}(x-4)} dx$
Dec
6
revised Closed form for Euler sum with $H_{2n}$?.
fix typo
Dec
6
revised Closed form for Euler sum with $H_{2n}$?.
added more information
Dec
6
awarded  Custodian
Dec
6
reviewed Approve Closed form for Euler sum with $H_{2n}$?.
Dec
6
comment Closed form for Euler sum with $H_{2n}$?.
I emended the heading to be more specific about what I was asking.
Dec
6
revised Closed form for Euler sum with $H_{2n}$?.
edited title
Dec
6
comment Closed form for Euler sum with $H_{2n}$?.
Yes, of course. Can anyone find a closed form for said Euler sum?.
Dec
6
asked Closed form for Euler sum with $H_{2n}$?.
Dec
3
comment another product of log integral
Hey nospoon, here is another integral I found if you're interested. I think it can be done the way you done the last one. But, I found: $$\int_{0}^{1}\log(1-x^{3})\log(1+x^{3})dx=1/4\left(-72+2 \gamma^{2}+\pi^{2}+4 \gamma \psi(1/6)+2\psi(1/6)-2\psi_{1}(7/6)\right)-\frac{1}{2}\left(3\sqrt{3}\pi +\frac{\pi^{2}}{6}+9\log(3)+12\log(2)-36\right)-\sum_{n=1}^{\infty}\frac{H_{2n}}‌​{(n(6n+1))}$$. I got stuck on that last sum....so far.
Dec
3
comment another product of log integral
Wow, thanks nospoon. Very nice work. There are lots of polylog identities. Maybe reference to Lewin's book we can find a way to simplify them. I managed to discover a solution, but it is not as efficient as yours. As mentioned above, I used a bunch of Euler sums.
Dec
3
accepted another product of log integral
Nov
29
revised another product of log integral
added another sum.