Timeline for A recursive formula
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Aug 2, 2018 at 15:22 | vote | accept | Dimitris Valianatos | ||
| Aug 2, 2018 at 1:26 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
[does the formula related]--->[does the formula relate]
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| Aug 1, 2018 at 18:51 | history | edited | GH from MO |
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| Aug 1, 2018 at 10:48 | answer | added | GH from MO | timeline score: 16 | |
| Aug 1, 2018 at 7:49 | comment | added | Dimitris Valianatos | Some numerical examples: For k=10 s=1.6767863973091431 and 1/s/exp(1)=0.2193 955304991764469019603 For k=50 s=1.6768750281592807 and 1/s/exp(1)=0.21938393439 80609892988775 For k=100 s=1.6768750281787006 and 1/s/exp(1)=0.2193839343955202 960012839 For k=1000 s=1.67687502817870086844136127504172485846 and 1/s/exp(1)= 0.219383934395520273677163775460121649031 (39 digits and more accuracy) We see that for higher values of k, we find more accuracy in decimal placies. So we can say that 1000 is "quite high" for a good approach. | |
| Aug 1, 2018 at 7:47 | comment | added | Dimitris Valianatos | I will give an example in (PARI): The recursive formula is s=1+n * s/(n+s), with initial value for s=1. eint1(1)= 0.219383934395520273677163775460121649031 Let a(k)=s=1.0;forstep(n=k,1,-1,s=1+n * s/(n+s));return(s) | |
| Aug 1, 2018 at 1:49 | comment | added | Alexey Ustinov | The queston is not clear. What it means "to start from quite high and finish at 1"? Both sequences A000262 and A002720 are mentioned in 10 entres in OEIS, did you check them? oeis.org/… | |
| S Aug 1, 2018 at 1:04 | history | suggested | B. Mehta |
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| Jul 31, 2018 at 22:35 | review | Suggested edits | |||
| S Aug 1, 2018 at 1:04 | |||||
| Jul 31, 2018 at 18:46 | comment | added | მამუკა ჯიბლაძე | Concerning the last one - it might help that this $a$ is given by the continued fraction$$1+\frac{1}{\frac{1}{1}+\frac{1}{1+\frac{1}{\frac{1}{2}+\frac{1}{1+\frac{1}{\frac{1}{3}+\frac{1}{1+\frac{1}{\frac{1}{4}+\frac{1}{1+\frac{1}{\frac{1}{5}+\frac{1}{1+\frac{1}{\frac{1}{6}+\frac{1}{1+\frac{1}{\frac{1}{7}+\cdots}}}}}}}}}}}}}$$ | |
| Jul 31, 2018 at 17:05 | history | edited | Dimitris Valianatos | CC BY-SA 4.0 |
added 18 characters in body
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| Jul 31, 2018 at 16:59 | history | edited | Dimitris Valianatos | CC BY-SA 4.0 |
added 22 characters in body
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| Jul 31, 2018 at 16:20 | history | asked | Dimitris Valianatos | CC BY-SA 4.0 |