42,935 reputation
1099183
bio website sites.google.com/site/…
location Canada
age
visits member for 4 years, 2 months
seen 27 mins ago

I am a graduate student in mathematics at Princeton university.

You can contact me at naslund [at] math [dot] princeton [dot] edu, or visit my website for more information.


5h
awarded  Necromancer
14h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 82 characters in body
16h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 4 characters in body
16h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 4 characters in body
17h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 276 characters in body
17h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 276 characters in body
18h
comment Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
Lastly, if you are skeptical, I have added several exact computations, and you may verify numerically that these are correct.
18h
comment Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
@columbus8myhw: Yes, the rational number $c/d$ should be in lowest terms. I have added that. It cannot equal $1$, as the proof would breakdown in that case. I added the slightly stronger condition that in lowest terms, at least one of $c,d$ must be even. This is because I did not want to deal with the partial fraction expansion when there is a double root at $x=0$. It should not take much more work extend this result to all rational numbers, but the form may be slightly different when both $c,d$ are odd.
18h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 449 characters in body
18h
comment Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
@columbus8myhw: I had never looked at this question before.
18h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 1298 characters in body
18h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 1298 characters in body
20h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
edited body
20h
comment Why does Titchmarsh say that we can move the derivative under $\frac{2}{\pi}\int_0^\infty \frac{\Xi(t)}{t^2 + \frac{1}{4}} \cosh(\alpha t) \, dt$
@nick corrected. Also I believe it is the second edition.
20h
revised Why does Titchmarsh say that we can move the derivative under $\frac{2}{\pi}\int_0^\infty \frac{\Xi(t)}{t^2 + \frac{1}{4}} \cosh(\alpha t) \, dt$
edited body
20h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 178 characters in body
21h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 57 characters in body
21h
revised Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
added 140 characters in body
21h
comment Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$
@anon: That doesn't look correct to me.
21h
answered Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$