Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen gezeigt.
| Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
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analyticalengine:bernoullinumbercalculation [2015-04-22 06:27] rainer layout, removed redundant nowikis |
analyticalengine:bernoullinumbercalculation [2015-08-26 11:23] (aktuell) rainer compacted B_7 example calculation |
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| Zeile 44: | Zeile 44: | ||
| Note that the signs are different to those in //Note G//. | Note that the signs are different to those in //Note G//. | ||
| + | |||
| + | ====== Why not equation 2 or 3? ====== | ||
| + | |||
| + | On page 725, AAL shows two commonly used formulas in equation 2 and 3, that do calculate the n-th Bernoulli number just as a series without recursion to other Bernoulli numbers, i.e. as a function of n alone. Then she writes: | ||
| + | > As however our object is not simplicity or facility of computation, but the illustration of the powers of the engine, we prefer selecting the formula below, marked (8.) | ||
| + | |||
| + | Thus she probably delibrately took into account the indexing problem. | ||
| + | |||
| + | While equation (2.) looks fairly simple, it is an inifinite sum of terms, which by itself would rule out using the AE. (Still need to write down examples, as elements to be summed up are not integer numbers.) | ||
| + | |||
| + | Equation (3.) looks like a finite sequence, but needs some rewriting to avoid arbitrary large numbers as intermediate results. (Would required deeper inspection too.) | ||
| + | |||
| + | So the version in equation (8.) looks to me the most simple soulution that has a facility of computation; so why did AAL deny this fairly good argument? | ||
| + | |||
| ====== The problem in line 21 ====== | ====== The problem in line 21 ====== | ||
| Zeile 99: | Zeile 113: | ||
| `A_5(4) = -14 * 5/5 * 4/6 = - 28/3` | `A_5(4) = -14 * 5/5 * 4/6 = - 28/3` | ||
| - | `B_7 = 7/18 - 4/6 + 14/30 - 28/(3*42) = (7 - 12)/18 + 7/15 - 14/63 = -5/18 + 7/15 - 14/63 = (-25 + 28)/90 + 14/63 = 17/90 -14/63 = (119 - 140 ) / (7*9*10) = - 21/(7*9*10) = - 1/30` | + | `B_7 = 7/18 - 4/6 + 14/30 - 28/(3*42) = (7 - 12)/18 + 7/15 - 2/9 = -5/18 + (21-10)/45 = (-25 + 22)/90 = -3/90 = - 1/30` |
