Timeline for Summation mollifier to ensure a certain alternating series has the correct value
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2014 at 23:57 | comment | added | Gottfried Helms | Very well; I use Euler-summation with configurable order. The order must be adapted: when the series to mollify is $1-1+1-1...$ order 1 is needed, when it is $1-3+9-27+81-...+...$ order 3 is needed and so on. If I see it correctly the current proposal is the matrix (or a matrix very near to that) for Euler-summation of order 1. But after your last formula it seems that you can circumvent quotients of absolute values $ \gt 1$, so that matrix should sufffice for all cases and no additional consideration is needed. | |
| Oct 1, 2014 at 20:35 | comment | added | John Jumper | I used a van Wijngaarden transformation and it worked extremely well. | |
| Oct 1, 2014 at 19:43 | comment | added | John Jumper | I should mention that I have a satisfactory solution, so please don't spend too much time on this. Thank you for the information though. | |
| Oct 1, 2014 at 19:37 | history | edited | John Jumper | CC BY-SA 3.0 |
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| Oct 1, 2014 at 18:35 | comment | added | Gottfried Helms | Hmm, if I understand things correctly it should be of vital interest how much the growth rate of the coefficients is which should be mollified (arithmetic/geometric/hypergeometric growth). The matrix given by Gerry Myerson can mollify geometric series with q=-2 at most. I think what you ask for is the transformation-matrix for Eulersummation (optimally: with configurable order). Is that correct so far? Second question: do you want to mollify the sequence of partial sums or the coefficients themselves? | |
| Oct 1, 2014 at 1:57 | vote | accept | John Jumper | ||
| Sep 30, 2014 at 23:55 | answer | added | Gerry Myerson | timeline score: 1 | |
| Sep 30, 2014 at 23:31 | answer | added | John Jumper | timeline score: 0 | |
| Sep 30, 2014 at 21:59 | history | asked | John Jumper | CC BY-SA 3.0 |