Timeline for A second-order recursion (functional equation)
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20 at 19:58 | vote | accept | Denis Serre | ||
| Feb 20 at 9:17 | answer | added | Fred Hucht | timeline score: 6 | |
| Feb 17 at 22:55 | comment | added | KStar | FWIW Mathematica gives $$L(s)=2^{s-3}\left(\left(\frac{17}{\sqrt{2}}-9\right)\Gamma\left(s+1\right)+\frac{17(-1)^s}{\sqrt{\pi}(s+1)}\Gamma\left(s+\frac{3}{2}\right){}_2F_1\left(1,s+\frac{3}{2};s+2;-1\right)\right).$$ | |
| Feb 17 at 18:00 | comment | added | Steven Stadnicki | This should succumb pretty easily to generating functions; you can get the $2s(2s+1)L(s-1)$ term by doing the usual differentiation (see e.g. section 2.4 of math.cmu.edu/~ploh/docs/math/2011-228/… ). This'll give you a second-order ODE for $\mathcal{L}(x)=\sum_nL(n)x^n$ that you may have more luck finding. | |
| Feb 17 at 16:59 | history | edited | Denis Serre | CC BY-SA 4.0 |
edited body
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| Feb 17 at 16:59 | comment | added | Denis Serre | @ChristianRemling Oups ! I fix it. Actually, it is $L(s-1)$ instead of $L(s+1)$ in the RHS. | |
| Feb 17 at 12:01 | history | asked | Denis Serre | CC BY-SA 4.0 |