Timeline for Is there any simpler form of this function
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 24, 2015 at 5:25 | comment | added | Robert Israel | $F(2n+1) = c_n + d_n \sqrt{2}$ where $$c_{{m}}={\frac {- \left( 4\,{m}^{2}+4\,m \right) c_{{m-2}}- \left( -6 \,{m}^{2}-5\,m+1 \right) c_{{m-1}}}{2\,{m}^{2}+m}} $$ and $$d_n = \dfrac{n!(n+1)!}{(2n+1)!} 2^{3n+1}$$ | |
| Mar 24, 2015 at 5:14 | comment | added | Robert Israel | It appears that $F(2n) = a_n + b_n \pi$ where $$a_n ={\frac {- \left( -2\,{n}^{2}+7\,n-6 \right) a _{ n-3} - \left( 9\,{n}^{2}-14\,n+7 \right) a _{ n-2 } - \left( -10\,{n}^{2}+10\,n \right) a_{ n-1} }{3 \,{n}^{2}-3\,n}} $$ while $$b_n = \dfrac{(2n+1)!}{(n!)^2 2^{n+2}}$$ | |
| Mar 23, 2015 at 22:17 | comment | added | user66638 | @Gerard No I cannot ;) | |
| Mar 23, 2015 at 21:52 | history | answered | Gerald Edgar | CC BY-SA 3.0 |