Rule: Q[2, 43, 46]

Type

This rule is of Legendre type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi 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 locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights
         plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
-0.99251333891064639124 + 6.8314924186348850609e-1847j 1.4e-477, 1.4e-477j
-0.95641845689756961284 - 7.2542913954984503938e-1849j 3.44e-478, 3.44e-478j
-0.92080137771891728617 - 6.4933496685209754037e-1850j 4.39e-479, 4.39e-479j
-0.99616649334628938703 - 3.1951254464922054555e-1847j 1.24e-477, 1.24e-477j
0.90668073304526380272 - 3.3238100426027881706e-1850j 1.99e-479, 1.99e-479j
0.95641845689756961284 - 1.2023336043280550855e-1848j 3.57e-478, 3.57e-478j
0.94568715750929023396 - 1.1504120150259611157e-1867j 1.87e-478, 1.87e-478j
-0.90668073304526380272 - 1.8010138681734548773e-1886j 1.84e-479, 1.84e-479j
-0.94568715750929023396 - 1.3836795569260411992e-1883j 1.82e-478, 1.82e-478j
0.99251333891064639124 + 6.4331556701962145022e-1887j 1.4e-477, 1.4e-477j
0.89147285941860497123 - 1.4290674190067167401e-1907j 7.36e-480, 7.36e-480j
-0.9985775575962523987 - 2.8270830228008511255e-1909j 8.92e-478, 8.92e-478j
-0.93381151762003847784 + 9.8731667391833853844e-1929j 9.43e-479, 9.43e-479j
-0.85785449441437768385 - 1.8825400419450169568e-1939j 8.09e-481, 8.09e-481j
0.9985775575962523987 - 1.2791784378750397891e-1934j 8.99e-478, 8.99e-478j
0.83948846396017340543 + 1.226935802127980057e-1955j 2.51e-481, 2.51e-481j
0.92080137771891728617 + 3.9145293751568299912e-1952j 4.29e-479, 4.29e-479j
-0.99976384899202477123 + 1.7114309791498154834e-1954j 3.45e-478, 3.45e-478j
-0.77847215819776463458 + 4.2244545168902281923e-1974j 4.17e-483, 4.17e-483j
-0.7997754664959359238 - 5.9560358040936066718e-1973j 1.75e-482, 1.75e-482j
0.93381151762003847784 - 4.7054961590525060313e-1967j 9.44e-479, 9.44e-479j
0.77847215819776463458 - 1.1537444129291859822e-1988j 3.92e-483, 3.92e-483j
0.99976384899202477123 - 6.5511719978696285811e-1991j 3.41e-478, 3.41e-478j
-0.87519182576232323891 - 1.9949614807769461574e-2026j 2.54e-480, 2.54e-480j
-0.83948846396017340543 - 1.4566784058649032473e-2031j 2.53e-481, 2.53e-481j
0.98163636878709305279 + 4.1725864365909400562e-2026j 1.11e-477, 1.11e-477j
0.75624389780534385877 + 7.2997253260051152827e-2046j 8.99e-484, 8.99e-484j
0.87519182576232323891 - 6.8132851316121524075e-2042j 2.54e-480, 2.54e-480j
0.99616649334628938703 - 6.570354182698703817e-2038j 1.25e-477, 1.25e-477j
-0.63229874064839623649 - 1.2529333493106880533e-2057j 1.18e-487, 1.18e-487j
0.6586884128783985472 + 1.0227012589140487825e-2057j 7.66e-487, 7.66e-487j
0.85785449441437768385 + 1.7696993564954506529e-2051j 8.15e-481, 8.15e-481j
0.73312362229052634202 - 4.0350895230439905685e-2055j 1.73e-484, 1.73e-484j
-0.98766473609786761411 + 1.8790228773620480446e-2045j 1.35e-477, 1.35e-477j
-0.73312362229052634202 - 4.3824192379903547731e-2057j 1.74e-484, 1.74e-484j
-0.70913773913876248798 - 9.2118354834521968192e-2058j 3.18e-485, 3.18e-485j
0.96600066996689792162 + 8.1403497877584775977e-2048j 5.64e-478, 5.64e-478j
0.63229874064839623649 - 1.736051668564887067e-2070j 1.14e-487, 1.14e-487j
0.8201218181824445892 + 7.2504324150659184083e-2063j 6.81e-482, 6.81e-482j
0.98766473609786761411 + 8.2060978414719721489e-2059j 1.33e-477, 1.33e-477j
-0.57735026918962576451 + 4.190020996578736256e-2079j 1.68e-489, 1.68e-489j
-0.96600066996689792162 + 2.5571329340089147212e-2065j 5.38e-478, 5.38e-478j
0.70913773913876248798 - 1.3701155970074026438e-2077j 3.08e-485, 3.08e-485j
0.68431388858078010034 + 2.1799755936268024164e-2078j 5.39e-486, 5.39e-486j
-0.75624389780534385877 - 1.1511463485976506498e-2073j 8.5e-484, 8.5e-484j
-0.60517556826906221022 + 1.6442551503197809603e-2079j 1.48e-488, 1.48e-488j
-0.68431388858078010034 + 4.1436077750619169816e-2077j 5.37e-486, 5.37e-486j
-0.98163636878709305279 + 4.7960379875127003342e-2068j 1.14e-477, 1.14e-477j
0.49005892454769074722 - 4.6876876251168770299e-2087j 1.81e-492, 1.81e-492j
0.97441465326648383555 - 5.8023041114496571248e-2073j 7.94e-478, 7.94e-478j
-0.6586884128783985472 + 5.3641217235565295639e-2085j 7.9e-487, 7.9e-487j
-0.51975463923876199007 + 5.14996448039780272e-2090j 1.99e-491, 1.99e-491j
0.7997754664959359238 - 1.8235882347585116629e-2082j 1.77e-482, 1.77e-482j
0.51975463923876199007 - 6.2438143348678988686e-2092j 1.93e-491, 1.93e-491j
0.60517556826906221022 - 1.4534650352335166351e-2088j 1.49e-488, 1.49e-488j
-0.8201218181824445892 - 9.3733875006987758233e-2079j 7.06e-482, 7.06e-482j
-0.49005892454769074722 - 2.1615427448736545937e-2091j 1.76e-492, 1.76e-492j
-0.89147285941860497123 - 4.9634251883968052495e-2076j 7.24e-480, 7.24e-480j
0.16919924017657105583 + 9.2497931784541199185e-2105j 2.4e-504, 2.4e-504j
0.39781962692582096067 + 1.575379357158684042e-2095j 8.97e-496, 8.97e-496j
-0.97441465326648383555 + 3.3401393861928431736e-2100j 8.55e-478, 8.55e-478j
-0.54886291856218829346 + 7.0306269812404975395e-2116j 1.86e-490, 1.86e-490j
-0.39781962692582096067 - 1.9304219157965906324e-2120j 9.41e-496, 9.41e-496j
0.13556491039604680337 + 2.104478641402377655e-2132j 1.16e-505, 1.16e-505j
0.42904840904179944423 - 2.9893034923480777316e-2119j 1.18e-494, 1.18e-494j
0.54886291856218829346 + 2.3896580439281270132e-2114j 1.92e-490, 1.92e-490j
-0.26894321002882683188 + 1.9316507856677288225e-2127j 1.55e-500, 1.55e-500j
-0.36615721759053762823 + 9.4100172535960481682e-2123j 6.5e-497, 6.5e-497j
-0.13556491039604680337 + 5.5028171726971785308e-2131j 1.2e-505, 1.2e-505j
0.57735026918962576451 - 1.0137024029601195901e-2121j 1.68e-489, 1.68e-489j
0.33409475817458540917 - 3.0355917096154451214e-2130j 4.2e-498, 4.2e-498j
0.10179476546176839672 + 8.1571596451905224827e-2139j 5.53e-507, 5.53e-507j
-0.42904840904179944423 + 9.6553055448134059956e-2124j 1.17e-494, 1.17e-494j
-0.33409475817458540917 - 3.4072002486180745874e-2128j 4.21e-498, 4.21e-498j
2.7087976584422146513e-2192 - 1.3560136673198522447e-2192j 2.76e-2190, 2.76e-2190j
0.36615721759053762823 + 2.9203642759142125241e-2129j 6.54e-497, 6.54e-497j
0.45980931128676297385 + 3.1045107691072583445e-2125j 1.67e-493, 1.67e-493j
-0.033972205229635101075 - 7.5270188636365512096e-2141j 1.45e-509, 1.45e-509j
-0.30167554181847803937 + 9.094539088224883736e-2130j 2.64e-499, 2.64e-499j
-0.45980931128676297385 - 1.0951259544406923468e-2123j 1.47e-493, 1.47e-493j
0.20266836641710813548 - 1.4665605544240990251e-2134j 4.19e-503, 4.19e-503j
0.30167554181847803937 + 9.7009368899146147393e-2133j 2.65e-499, 2.65e-499j
0.033972205229635101075 + 4.175779956515389365e-2141j 1.15e-509, 1.15e-509j
-0.16919924017657105583 - 7.0214418805256039911e-2135j 2.28e-504, 2.28e-504j
-0.20266836641710813548 - 7.8936946317371357412e-2134j 4.65e-503, 4.65e-503j
0.067917141529800287122 - 1.3350534329843087373e-2139j 2.37e-508, 2.37e-508j
0.26894321002882683188 - 2.6450371996496466938e-2133j 1.56e-500, 1.56e-500j
0.23593036010989067891 + 1.052674436069932029e-2133j 8.73e-502, 8.73e-502j
-0.10179476546176839672 - 1.7489095416156005227e-2137j 5.41e-507, 5.41e-507j
-0.23593036010989067891 + 2.9614613171299058149e-2133j 8.36e-502, 8.36e-502j
-0.067917141529800287122 + 3.1740058851595431152e-2139j 2.54e-508, 2.54e-508j

Weights

Weight (ball center) Error (ball radius)
0.0042574441594840598167 + 4.732362623150094674e-1847j 3.19e-126, 2.94e-355j
0.010158377835935056782 - 2.9032707702287940803e-1847j 1.55e-126, 1.43e-355j
0.013569988936368698653 + 2.0991719541364176537e-1847j 6.68e-127, 6.15e-356j
0.0030396159091161961445 + 5.1353861784378234844e-1847j 3.34e-127, 3.08e-356j
0.01466723350870352008 - 4.9977181860354116789e-1849j 1.6e-128, 1.47e-357j
0.010158377835935056782 - 4.7544289690455454736e-1849j 6.54e-129, 6.03e-358j
0.011303895647826391972 - 6.454331719915871805e-1849j 6.98e-129, 6.44e-358j
0.01466723350870352008 - 1.9279369477517285072e-1847j 1.67e-127, 1.54e-356j
0.011303895647826391972 + 2.6194226749228722411e-1847j 2.49e-127, 2.29e-356j
0.0042574441594840598167 + 3.5139940559346215791e-1849j 2.21e-131, 2.03e-360j
0.015746458115432337345 + 6.2023053710597703986e-1849j 1.91e-129, 1.76e-358j
0.0017815018839717834762 - 4.576806353188827011e-1847j 4.2e-128, 3.87e-357j
0.012445935091027063992 - 2.320970836647768994e-1847j 1.48e-127, 1.36e-356j
0.017856837795114958247 + 1.6057018231281123682e-1847j 4.24e-130, 3.91e-359j
0.0017815018839717834762 + 1.4552628319305070878e-1849j 2.99e-132, 2.76e-361j
0.018870365920211484378 - 1.0507723165552016557e-1848j 2.35e-132, 2.17e-361j
0.013569988936368698653 + 3.4406694119302712731e-1849j 8.26e-131, 7.61e-360j
0.00063606888329957536401 + 1.162145981521106322e-1847j 3.56e-129, 3.28e-358j
0.021771655852080997288 + 1.3778332851952321577e-1847j 3.03e-133, 2.79e-362j
0.020829427810723277772 - 1.4210153160115694667e-1847j 6.01e-133, 5.54e-362j
0.012445935091027063992 - 4.2617137007776754775e-1850j 4.68e-131, 4.31e-360j
0.021771655852080997288 + 1.4792422023224513869e-1848j 9.75e-135, 8.98e-364j
0.00063606888329957536401 - 4.898414701058991829e-1850j 7.47e-133, 6.88e-362j
0.016812978855168948563 - 1.6936285193043475714e-1847j 7.92e-132, 7.3e-361j
0.018870365920211484378 - 1.533115518519215331e-1847j 1.65e-132, 1.52e-361j
0.0066227240797830761603 + 6.5599842934082024727e-1849j 2.51e-133, 2.31e-362j
0.0226791997811977089 - 1.636383377560929985e-1848j 2.87e-136, 2.64e-365j
0.016812978855168948563 - 7.7562309473357199708e-1849j 7.73e-134, 7.13e-363j
0.0030396159091161961445 - 2.4275709431228702648e-1849j 4.34e-133, 4e-362j
0.02676113893125857767 + 1.2361779658850575829e-1847j 8.79e-141, 8.1e-370j
0.026013265303190652434 - 2.3740754478368755025e-1848j 2e-139, 1.85e-368j
0.017856837795114958247 + 9.1457310938955029237e-1849j 1.48e-134, 1.36e-363j
0.023557135446865437607 + 1.8031793325757924751e-1848j 1.45e-137, 1.33e-366j
0.0054372743342730251225 - 9.8343993915397549849e-1847j 3.93e-136, 3.62e-365j
0.023557135446865437607 + 1.3120367764801069728e-1847j 8.35e-140, 7.7e-369j
0.024410201905632847558 - 1.2868551589178307847e-1847j 2.1e-140, 1.94e-369j
0.0090026713878182580438 + 1.6010645181840318881e-1848j 1.92e-135, 1.77e-364j
0.02676113893125857767 + 2.5928565764333220675e-1848j 8.24e-142, 7.59e-371j
0.019859657410444026311 + 1.1886794967804446791e-1848j 1.14e-137, 1.05e-366j
0.0054372743342730251225 - 4.8349038850491319401e-1849j 1.32e-135, 1.22e-364j
0.028163568993709169178 + 1.217189337737456723e-1847j 1.12e-145, 1.03e-374j
0.0090026713878182580438 + 3.3452960382342686274e-1847j 1.68e-140, 1.55e-369j
0.024410201905632847558 - 1.980532329602618711e-1848j 2.12e-140, 1.96e-369j
0.025231261701817050601 + 2.1702216625443124107e-1848j 4.33e-141, 3.99e-370j
0.0226791997811977089 - 1.3419791336147753348e-1847j 2.51e-142, 2.31e-371j
0.027480170117693233672 - 1.2254614431889408966e-1847j 8.92e-146, 8.22e-375j
0.025231261701817050601 + 1.2660963761348560664e-1847j 1.76e-144, 1.62e-373j
0.0066227240797830761603 + 5.7439377193328188577e-1847j 4.49e-142, 4.14e-371j
0.029978971648656627787 - 3.9491758477581450664e-1848j 5.2e-150, 4.79e-379j
0.0078206416256476531196 - 9.2745487331154653495e-1849j 2.91e-139, 2.68e-368j
0.026013265303190652434 - 1.2494765047555800615e-1847j 3.39e-145, 3.12e-374j
0.029407087467856154864 + 1.206911786301826513e-1847j 7.7e-150, 7.1e-379j
0.020829427810723277772 - 1.3307014103381779903e-1848j 2.11e-142, 1.94e-371j
0.029407087467856154864 + 3.6397321367676462716e-1848j 3.57e-150, 3.29e-379j
0.027480170117693233672 - 2.8271884835670526188e-1848j 6.44e-148, 5.93e-377j
0.019859657410444026311 + 1.4724079243346474443e-1847j 3.69e-144, 3.4e-373j
0.029978971648656627787 - 1.2035582055812383233e-1847j 3.96e-151, 3.65e-380j
0.015746458115432337345 + 1.799979288778315596e-1847j 5.88e-144, 5.42e-373j
0.033557715185015499901 - 8.0259974130899259379e-1848j 1.02e-156, 9.4e-386j
0.031450685993289451463 + 5.0033608229399971192e-1848j 2.16e-154, 1.99e-383j
0.0078206416256476531196 - 4.2033889043816069827e-1847j 1.02e-143, 9.39e-373j
0.02880407013828086872 - 1.2112306983028951265e-1847j 1.77e-149, 1.63e-378j
0.031450685993289451463 + 1.1973025436150718145e-1847j 1.58e-154, 1.45e-383j
0.033706319554066008246 + 8.4759163381666202072e-1848j 1.53e-157, 1.41e-386j
0.031001369408647644378 - 4.631020200523680995e-1848j 2.37e-154, 2.18e-383j
0.02880407013828086872 - 3.349585089292091058e-1848j 4.42e-152, 4.08e-381j
0.032877274038600600062 + 1.1793020555363244607e-1847j 3.63e-158, 3.35e-387j
0.031868790049665741023 - 1.194622702043753676e-1847j 2.42e-156, 2.23e-385j
0.033706319554066008246 + 1.1232156139497940725e-1847j 8.38e-160, 7.73e-389j
0.028163568993709169178 + 3.07882951920859055e-1848j 1.31e-152, 1.2e-381j
0.032248694092781591517 + 5.8032295002325723841e-1848j 6.09e-158, 5.61e-387j
0.03382955999087260431 - 8.9121706841150763721e-1848j 1.04e-159, 9.6e-389j
0.031001369408647644378 - 1.1991883079774872412e-1847j 1.66e-156, 1.53e-385j
0.032248694092781591517 + 1.1909539912476189607e-1847j 4.13e-158, 3.8e-387j
0.033975987229429753894 + 1.0100916629779009164e-1847j 1.57e-161, 1.44e-390j
0.031868790049665741023 - 5.394185191099351777e-1848j 1.52e-158, 1.4e-387j
0.030512959965073494732 + 4.2792120081755942067e-1848j 5.36e-157, 4.94e-386j
0.033964185058657106484 - 1.0436748669132021287e-1847j 5.14e-162, 4.74e-391j
0.032582188797674865937 - 1.1861073682167820089e-1847j 4.48e-160, 4.13e-389j
0.030512959965073494732 + 1.201032731924598137e-1847j 5.05e-158, 4.65e-387j
0.033373245775857303069 + 7.5707341097750227732e-1848j 8.16e-162, 7.52e-391j
0.032582188797674865937 - 6.2298755202471524027e-1848j 3.56e-161, 3.28e-390j
0.033964185058657106484 - 9.7299930578988235332e-1848j 1.09e-162, 1e-391j
0.033557715185015499901 - 1.1420489483606636582e-1847j 1.84e-163, 1.7e-392j
0.033373245775857303069 + 1.157362894556712023e-1847j 2.02e-163, 1.86e-392j
0.033918705860862156685 + 9.3311708484168437728e-1848j 3.6e-163, 3.32e-392j
0.032877274038600600062 + 6.6698486358729722846e-1848j 2.14e-163, 1.97e-392j
0.033143486135632337625 - 7.117704295754695053e-1848j 1.61e-163, 1.48e-392j
0.03382955999087260431 - 1.1003586635326782527e-1847j 2.8e-165, 2.58e-394j
0.033143486135632337625 - 1.169761897424293655e-1847j 2.48e-165, 2.33e-394j
0.033918705860862156685 + 1.0737235162255069007e-1847j 2.83e-165, 2.6e-394j

Download

All rules of Legendre type can be downloaded here packed into a single file.