One starts from the polynomial
and extends one by one with
until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size!
The complete polynomials are included in the download.
| Node (ball center) | Error (ball radius) |
|---|---|
| -0.99970410104391670461 + 2.9281516031092421474e-846j | 1.15e-229, 1.15e-229j |
| -0.98468195927199447623 + 4.2551488569953280681e-848j | 2.18e-229, 2.18e-229j |
| -0.9225217132136291628 - 6.6580548003710193558e-851j | 2.51e-231, 2.51e-231j |
| -0.99823057474573572479 - 2.8115529165632471873e-847j | 2.73e-229, 2.73e-229j |
| 0.95417744289591430055 - 2.5210751208383335052e-848j | 1.96e-230, 1.96e-230j |
| 0.93950036120944049357 - 7.6794326539840910141e-851j | 7.37e-231, 7.37e-231j |
| 0.99527136786624958644 + 1.0481965585572653401e-852j | 3.4e-229, 3.4e-229j |
| -0.93950036120944049357 - 2.4857854231053725488e-883j | 7.17e-231, 7.17e-231j |
| 0.99079325588510780584 + 2.0884388583859230814e-879j | 2.82e-229, 2.82e-229j |
| 0.99823057474573572479 - 1.3890419721407401379e-897j | 2.85e-229, 2.85e-229j |
| 0.88177827725295929029 + 2.2028724988912972129e-922j | 1.89e-232, 1.89e-232j |
| 0.99970410104391670461 + 2.6664687925765596801e-916j | 1e-229, 1e-229j |
| -0.88177827725295929029 - 4.4620641454851102273e-930j | 1.96e-232, 1.96e-232j |
| -0.85810591605597981957 + 3.1558047289507118145e-930j | 5.03e-233, 5.03e-233j |
| 0.70921295863303400043 + 1.2765785333717816991e-936j | 8.2e-237, 8.2e-237j |
| 0.85810591605597981957 + 1.1617610693394554742e-931j | 4.62e-233, 4.62e-233j |
| 0.90326723171240018946 - 1.1417734050474316806e-929j | 7.88e-232, 7.88e-232j |
| -0.99527136786624958644 + 4.1077321930853912397e-925j | 3.22e-229, 3.22e-229j |
| -0.77459666924148337704 - 6.3364680015503374426e-934j | 3.61e-235, 3.61e-235j |
| -0.95417744289591430055 - 8.7993415007740551835e-930j | 2.1e-230, 2.1e-230j |
| 0.9225217132136291628 + 3.5355700626673026535e-929j | 2.4e-231, 2.4e-231j |
| 0.77459666924148337704 - 4.3213227709762079557e-933j | 3.49e-235, 3.49e-235j |
| -0.96655433101153010644 - 5.4015118595206751204e-929j | 5.15e-230, 5.15e-230j |
| -0.83230817570307920397 - 8.1785036851370554074e-933j | 1.07e-233, 1.07e-233j |
| -0.80444880898222963771 + 2.1846572090709997379e-933j | 2.03e-234, 2.03e-234j |
| -0.97667972251506854616 - 1.2451468288317258587e-927j | 1.06e-229, 1.06e-229j |
| 0.74282534743536069472 - 7.8291413622391976551e-935j | 5.9e-236, 5.9e-236j |
| 0.96655433101153010644 + 3.908749976096527204e-926j | 5.36e-230, 5.36e-230j |
| -0.99079325588510780584 + 3.4135583144972038289e-937j | 2.98e-229, 2.98e-229j |
| -0.6367993325216061138 - 6.2233965611352898691e-948j | 1.22e-238, 1.22e-238j |
| -0.24444856241006580723 + 5.5188192076498657965e-958j | 5.5e-249, 5.5e-249j |
| 0.80444880898222963771 - 4.078259104018402483e-942j | 2.01e-234, 2.01e-234j |
| 0.67384201563671628051 + 2.3942626363834310468e-946j | 1.1e-237, 1.1e-237j |
| 0.98468195927199447623 + 1.6738739730795945809e-940j | 2e-229, 2e-229j |
| -0.5981759193301111904 - 9.3462050837737969523e-966j | 1.29e-239, 1.29e-239j |
| -0.74282534743536069472 + 8.4899655528235266492e-965j | 5.69e-236, 5.69e-236j |
| 0.97667972251506854616 - 2.087743069857858462e-962j | 1.2e-229, 1.2e-229j |
| 0.6367993325216061138 + 3.9472411872446608817e-974j | 1.24e-238, 1.24e-238j |
| 0.83230817570307920397 - 1.6636507475590324344e-969j | 1.04e-233, 1.04e-233j |
| -0.70921295863303400043 + 1.4785534391912417583e-969j | 8.04e-237, 8.04e-237j |
| -0.55806685067819680295 + 1.5842256814047331219e-973j | 1.29e-240, 1.29e-240j |
| -0.90326723171240018946 - 3.4299902731716952273e-976j | 7.21e-232, 7.21e-232j |
| 0.55806685067819680295 + 1.578790102911961532e-986j | 1.17e-240, 1.17e-240j |
| 0.51657109968341089508 + 7.0647496722274393643e-988j | 1.02e-241, 1.02e-241j |
| 0.098634553014592439996 + 1.6935802987852072698e-998j | 5.08e-253, 5.08e-253j |
| -0.51657109968341089508 + 8.5990102368390608252e-986j | 1.05e-241, 1.05e-241j |
| -0.67384201563671628051 + 1.2364971345569420066e-986j | 1.12e-237, 1.12e-237j |
| 0.049378511602724708577 - 3.1561749973669306165e-1003j | 2.46e-254, 2.46e-254j |
| 0.47379132949741309452 + 3.7946769051348225165e-990j | 8.04e-243, 8.04e-243j |
| 0.5981759193301111904 - 3.1634613133516442248e-991j | 1.32e-239, 1.32e-239j |
| -0.33882426570083056354 + 3.6912376882969083691e-997j | 2.06e-246, 2.06e-246j |
| -0.47379132949741309452 - 5.8269568543771188961e-994j | 7.81e-243, 7.81e-243j |
| -0.1476459082052927976 + 1.8489027523895688903e-1002j | 1.12e-251, 1.12e-251j |
| 0.33882426570083056354 - 1.0699530384406716304e-998j | 1.98e-246, 1.98e-246j |
| 0.38480726695303768366 + 6.5810866093228557165e-997j | 3.3e-245, 3.3e-245j |
| -1.0385986179676208168e-1045 - 2.5888174136815004642e-1045j | 1.87e-1043, 1.87e-1043j |
| -0.42983363895728045028 - 5.687182765347511355e-995j | 5.26e-244, 5.26e-244j |
| -0.2919991541426287378 - 1.5180568417514668141e-998j | 1.15e-247, 1.15e-247j |
| 0.1476459082052927976 - 6.2931867743329642928e-1003j | 9.9e-252, 9.9e-252j |
| 0.42983363895728045028 + 2.4206917622643848344e-995j | 5.42e-244, 5.42e-244j |
| 0.19629087859904982233 + 2.9610367033581806679e-1001j | 2.71e-250, 2.71e-250j |
| -0.19629087859904982233 - 7.6734185282287559985e-1001j | 2.53e-250, 2.53e-250j |
| -0.38480726695303768366 - 3.6622043253727634118e-998j | 3.54e-245, 3.54e-245j |
| -0.049378511602724708577 - 2.1489881534529798466e-1005j | 2.46e-254, 2.46e-254j |
| 0.24444856241006580723 - 3.6157940499935376902e-1000j | 5.31e-249, 5.31e-249j |
| 0.2919991541426287378 + 1.1300646536893500084e-998j | 1.15e-247, 1.15e-247j |
| -0.098634553014592439996 - 4.3837998651949276395e-1004j | 4.8e-253, 4.8e-253j |
| Weight (ball center) | Error (ball radius) |
|---|---|
| 0.0007953830760179075773 + 2.8835093894009437506e-846j | 1.88e-23, 1.89e-130j |
| 0.0070104091656751119795 + 6.5538755445329193406e-847j | 3.96e-24, 4e-131j |
| 0.018122426792585656544 - 3.1704158814602976909e-848j | 1e-24, 1.01e-131j |
| 0.0022009833498934978465 - 4.4280058926198842849e-846j | 1.35e-23, 1.37e-130j |
| 0.013523670782711931926 - 1.2306971728212632015e-848j | 1.22e-25, 1.24e-132j |
| 0.015830396101133155688 - 1.5346340426735458959e-848j | 1.01e-25, 1.02e-132j |
| 0.0037153368653435579011 + 2.4337870817546119828e-848j | 1.01e-26, 1.02e-133j |
| 0.015830396101133155688 + 5.4771156283641404263e-848j | 3.22e-26, 3.25e-133j |
| 0.0052591624859932865213 - 2.9073614228070759427e-848j | 6.29e-27, 6.36e-134j |
| 0.0022009833498934978465 - 1.623201753757708536e-848j | 2.93e-27, 2.96e-134j |
| 0.022589806317219724164 + 7.4144288287591087935e-850j | 1.06e-30, 1.07e-137j |
| 0.0007953830760179075773 + 5.7035504910919549783e-849j | 1.44e-27, 1.46e-134j |
| 0.022589806317219724164 - 1.2227808920758195673e-848j | 1.68e-31, 1.69e-138j |
| 0.024745226231400873948 + 8.0698537738751983819e-849j | 7.09e-32, 7.16e-139j |
| 0.034505779650501820651 - 1.3026555884903657082e-850j | 8.21e-34, 8.29e-141j |
| 0.024745226231400873948 - 2.8655846902655652414e-850j | 2.84e-32, 2.87e-139j |
| 0.020379549844067645494 - 1.781053743834741799e-849j | 1.78e-31, 1.8e-138j |
| 0.0037153368653435579011 + 2.3371096226309126727e-846j | 5.75e-32, 5.81e-139j |
| 0.030824378168674219199 - 2.8315813886985859735e-849j | 5.12e-36, 5.17e-143j |
| 0.013523670782711931926 - 9.9621880117971606599e-848j | 3.13e-33, 3.16e-140j |
| 0.018122426792585656544 + 4.5464727795331438588e-849j | 1.83e-33, 1.85e-140j |
| 0.030824378168674219199 - 9.0842451437454257509e-851j | 6.72e-37, 6.79e-144j |
| 0.011237673675994406662 + 1.8969976973322599919e-847j | 2.08e-33, 2.1e-140j |
| 0.026839619292757064696 - 5.520126710695518544e-849j | 4.72e-36, 4.77e-143j |
| 0.028867632734499652369 + 3.8979936440168761904e-849j | 9.88e-37, 9.98e-144j |
| 0.0090338343941237849284 - 3.7745812636699240583e-847j | 1.31e-33, 1.32e-140j |
| 0.032705244305957020794 + 1.177130917738644037e-850j | 1.85e-39, 1.87e-146j |
| 0.011237673675994406662 + 4.0791688693729564348e-848j | 1.21e-36, 1.22e-143j |
| 0.0052591624859932865213 - 1.1955756112510602417e-846j | 1.49e-33, 1.51e-140j |
| 0.037848560108731145407 - 9.923866636850043656e-850j | 3.54e-42, 3.57e-149j |
| 0.047873998297058339519 + 2.3761604426434095805e-850j | 4.44e-45, 4.48e-152j |
| 0.028867632734499652369 + 3.6755723201401775724e-851j | 1.88e-39, 1.9e-146j |
| 0.03622163560819422054 + 1.3521905320415067359e-850j | 7.2e-42, 7.27e-149j |
| 0.0070104091656751119795 + 3.071546532024808219e-848j | 4.35e-37, 4.39e-144j |
| 0.039382417757958066764 + 8.007527251151722475e-850j | 2.26e-44, 2.29e-151j |
| 0.032705244305957020794 + 2.1096999687537116666e-849j | 4.53e-42, 4.58e-149j |
| 0.0090338343941237849284 - 3.1880827596007937356e-848j | 2.44e-37, 2.47e-144j |
| 0.037848560108731145407 - 1.3620330424914544638e-850j | 2.21e-44, 2.23e-151j |
| 0.026839619292757064696 + 7.0503460810798690779e-851j | 2e-40, 2.02e-147j |
| 0.034505779650501820651 - 1.6081259263220791579e-849j | 2.38e-43, 2.41e-150j |
| 0.040819220562245432564 - 6.5658559824285265998e-850j | 4.48e-46, 4.52e-153j |
| 0.020379549844067645494 + 1.9297890260859205188e-848j | 4.56e-40, 4.61e-147j |
| 0.040819220562245432564 - 1.3346008835211586935e-850j | 3.39e-47, 3.42e-154j |
| 0.042155166650439025395 + 1.3154161812344863849e-850j | 4.16e-48, 4.2e-155j |
| 0.04915403352337792146 - 1.4358347234072222101e-850j | 4.58e-52, 4.63e-159j |
| 0.042155166650439025395 + 5.4648672976644827386e-850j | 1.7e-48, 1.72e-155j |
| 0.03622163560819422054 + 1.2514135990641785808e-849j | 1.63e-45, 1.64e-152j |
| 0.049337675590295678703 + 1.5028551056473473223e-850j | 1.17e-52, 1.18e-159j |
| 0.043386685628243512325 - 1.2987120141878995457e-850j | 5.67e-50, 5.73e-157j |
| 0.039382417757958066764 + 1.3523507175044644551e-850j | 1.48e-47, 1.5e-154j |
| 0.046423330721986493672 + 2.9935098180426995362e-850j | 3.72e-52, 3.76e-159j |
| 0.043386685628243512325 - 4.6126453076090213731e-850j | 2.39e-50, 2.41e-157j |
| 0.048848389116050906697 + 1.9653293048717713873e-850j | 1.24e-53, 1.25e-160j |
| 0.046423330721986493672 + 1.2833651364150028806e-850j | 1.33e-53, 1.34e-160j |
| 0.045523579339177354529 - 1.2813953213010233431e-850j | 4.66e-53, 4.71e-160j |
| 0.04939893170347493219 - 1.5861388324544901631e-850j | 1.21e-54, 1.22e-161j |
| 0.044510483497866468382 + 3.9449720682839930473e-850j | 9.17e-53, 9.26e-160j |
| 0.047207448126030162956 - 2.6527585057408932044e-850j | 9.12e-54, 9.21e-161j |
| 0.048848389116050906697 + 1.3829223175861688354e-850j | 1.8e-55, 1.82e-162j |
| 0.044510483497866468382 + 1.2868655804444583576e-850j | 3.49e-54, 3.53e-161j |
| 0.048421396386057486106 - 1.3424293739037240513e-850j | 6.23e-56, 6.28e-163j |
| 0.048421396386057486106 - 2.1503788147883401173e-850j | 7.86e-56, 7.91e-163j |
| 0.045523579339177354529 - 3.4162278125256372991e-850j | 4.56e-55, 4.61e-162j |
| 0.049337675590295678703 + 1.6884461506305301586e-850j | 1.22e-56, 1.24e-163j |
| 0.047873998297058339519 + 1.3130236300762750375e-850j | 4.58e-57, 4.74e-164j |
| 0.047207448126030162956 - 1.2936346818386002525e-850j | 4.74e-57, 4.94e-164j |
| 0.04915403352337792146 - 1.81332112777242591e-850j | 3.86e-57, 3.68e-164j |
All rules of Legendre type can be downloaded here packed into a single file.