Timeline for Seeking an integral formulation for an algebraic function
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2022 at 22:21 | comment | added | Peter Taylor | Generalising a bit further we have $$\frac 1{\pi \csc {k \pi}} \int_0^\infty \frac{t^k}{(t+a)(t+b)} \textrm{d}t = \frac{a^k - b^k}{a - b}$$ and $$\frac 1{\pi \csc {k \pi}} \int_0^\infty \frac{t^k}{(t+a)(t+b)(t+c)} \textrm{d}t = \frac{a^k (b - c) + b^k (c - a) + c^k (a - b)}{(a - b)(b - c)(c - a)}$$ but I'm not seeing how to use those to get the desired form with linear factors. | |
| Aug 5, 2022 at 19:02 | comment | added | T. Amdeberhan | This is nice and upvoted. But, is there some other ones with linear factors? | |
| Aug 4, 2022 at 10:20 | history | answered | Peter Taylor | CC BY-SA 4.0 |