Rule: Q[2, 4, 6, 22, 36]

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)
0.99835768318550801462 + 7.5932750345725886109e-825j 1.29e-229, 1.29e-229j
-0.9637327783385524226 - 8.1567608594176840856e-848j 1.05e-230, 1.05e-230j
-0.94932275186407481078 + 1.2827272359744956397e-847j 4.57e-231, 4.57e-231j
-0.99556714979976053988 + 5.5314316182616711663e-845j 1.3e-229, 1.3e-229j
0.89020694465909681935 - 8.6933585264354753465e-848j 1.9e-232, 1.9e-232j
0.94932275186407481078 + 1.7483127631079600215e-845j 4.35e-231, 4.35e-231j
0.99971035471794628499 - 2.1700322774588399394e-842j 5.26e-230, 5.26e-230j
-0.89020694465909681935 + 1.1730715758223977639e-858j 1.95e-232, 1.95e-232j
-0.1047836534213083021 - 1.0555477505771386421e-879j 6.52e-253, 6.52e-253j
-0.99971035471794628499 - 4.6054788203732977404e-853j 5.1e-230, 5.1e-230j
0.91248695683407599658 + 1.9069199227702987813e-857j 5.71e-232, 5.71e-232j
0.99105250481616767714 + 8.9315499173218220159e-854j 9.63e-230, 9.63e-230j
-0.93222133946433429354 - 2.0611415781509517576e-866j 1.59e-231, 1.59e-231j
-0.80949270909121460968 + 5.2662549343713285011e-869j 5.45e-234, 5.45e-234j
0.9637327783385524226 - 1.1625628754851227208e-864j 1.12e-230, 1.12e-230j
0.77873323893277110141 + 2.7156592507918840573e-869j 1.7e-234, 1.7e-234j
0.86549938609357694638 - 4.7772609506466841995e-868j 5.92e-233, 5.92e-233j
-0.98446790263660712388 + 2.6622091525233754982e-863j 5.49e-230, 5.49e-230j
-0.77873323893277110141 - 3.9199925737296656755e-871j 1.7e-234, 1.7e-234j
-0.91248695683407599658 + 7.7860161581112297027e-868j 5.93e-232, 5.93e-232j
0.83852207272926610089 + 2.1927088739848327168e-868j 1.76e-233, 1.76e-233j
0.80949270909121460968 - 1.6249888434678505931e-869j 5.8e-234, 5.8e-234j
-0.25746215955965288222 + 2.4458895898217255931e-884j 2.06e-248, 2.06e-248j
-0.86549938609357694638 - 3.7218273779532728613e-869j 5.8e-233, 5.8e-233j
-0.71458207458063436713 + 4.3264122681296925193e-871j 1.89e-235, 1.89e-235j
0.93222133946433429354 + 6.7469226800003453463e-866j 1.78e-231, 1.78e-231j
0.68401217235521649532 + 8.78941225872336493e-871j 8.44e-236, 8.44e-236j
0.71458207458063436713 - 3.8972389106531568036e-870j 1.91e-235, 1.91e-235j
-0.99835768318550801462 - 1.9575553065705134458e-866j 1.2e-229, 1.2e-229j
-0.63352702761174118591 + 1.9360258155241013204e-872j 1.07e-236, 1.07e-236j
-0.97543045249072415158 + 9.7114571370380319983e-866j 2.55e-230, 2.55e-230j
0.98446790263660712388 - 7.1980021414154136213e-863j 5.02e-230, 5.02e-230j
0.65734287249805013598 - 1.3128131675875684837e-883j 3.27e-236, 3.27e-236j
-0.74677180221832073614 + 9.8553145814494314787e-883j 5.52e-235, 5.52e-235j
-0.68401217235521649532 + 5.0335852306101938345e-884j 7.78e-236, 7.78e-236j
-0.65734287249805013598 - 3.4393472646432356175e-884j 3.23e-236, 3.23e-236j
0.74677180221832073614 + 2.7079215651679697671e-882j 5.49e-235, 5.49e-235j
0.57735026918962576451 - 9.221880599718242865e-888j 2.58e-238, 2.58e-238j
0.97543045249072415158 + 7.70637089350568444e-877j 2.77e-230, 2.77e-230j
-0.83852207272926610089 - 7.1637622099379676422e-892j 1.81e-233, 1.81e-233j
-0.54417719215067768367 - 7.9172290884752287275e-900j 2.58e-239, 2.58e-239j
-0.99105250481616767714 - 5.4163241167177674527e-896j 9.09e-230, 9.09e-230j
0.63352702761174118591 + 4.4696504189746661244e-917j 1.06e-236, 1.06e-236j
0.60768074044860834814 - 4.7841452529014593626e-919j 2.11e-237, 2.11e-237j
0.99556714979976053988 + 1.7500765694686219258e-926j 1.32e-229, 1.32e-229j
-0.57735026918962576451 + 5.8964168342946684594e-960j 2.59e-238, 2.59e-238j
-0.60768074044860834814 + 8.780762736603103179e-964j 2.04e-237, 2.04e-237j
0.39617701247318581351 + 8.6269424372155687334e-969j 5.37e-244, 5.37e-244j
0.47456704935223358268 + 3.0346977760543223232e-965j 1.81e-241, 1.81e-241j
0.3523124687524059471 - 1.3389051345786358873e-969j 2.06e-245, 2.06e-245j
-0.50992493118502290047 + 4.0642969211274278925e-966j 2.42e-240, 2.42e-240j
-0.47456704935223358268 - 1.8114522748679103056e-967j 1.98e-241, 1.98e-241j
-8.7315758759081504913e-05 + 1.9598993681475118687e-982j 1.68e-257, 1.68e-257j
0.54417719215067768367 + 2.1959924969855884277e-964j 2.6e-239, 2.6e-239j
0.50992493118502290047 - 4.406196660185717799e-971j 2.4e-240, 2.4e-240j
0.052513218848459454265 + 2.4582315429852280764e-985j 2.71e-254, 2.71e-254j
-0.43693939954921891801 - 5.8491762460882185238e-973j 1.16e-242, 1.16e-242j
-0.30587780828933154408 - 4.5929607315672586776e-978j 6.68e-247, 6.68e-247j
0.1047836534213083021 + 2.7635140703092571614e-983j 7.18e-253, 7.18e-253j
0.43693939954921891801 - 6.1498161235553785174e-974j 1.11e-242, 1.11e-242j
0.15655801081562154215 + 2.9593284522810091526e-982j 1.91e-251, 1.91e-251j
-0.15655801081562154215 - 9.0819674215593963098e-982j 1.95e-251, 1.95e-251j
-0.39617701247318581351 + 6.211426489147330105e-975j 5.6e-244, 5.6e-244j
-0.052513218848459454265 - 2.7517062419802667996e-985j 2.71e-254, 2.71e-254j
0.30587780828933154408 - 3.2529242670430185864e-977j 6.48e-247, 6.48e-247j
0.25746215955965288222 + 2.0605273137172983988e-978j 2.25e-248, 2.25e-248j
8.7315758759081504913e-05 + 2.9119347377400059403e-987j 1.68e-257, 1.68e-257j
-0.3523124687524059471 - 1.2161464254090623301e-975j 2.08e-245, 2.08e-245j
-0.20755811681584119858 + 6.5019664975007502439e-980j 6.17e-250, 6.17e-250j
0.20755811681584119858 + 1.6660684406848148661e-980j 6.31e-250, 6.31e-250j

Weights

Weight (ball center) Error (ball radius)
0.0020145241994806266316 - 6.6771560172620458995e-826j 2.95e-29, 2.5e-137j
0.013053172036381860951 - 3.8134429182840316505e-828j 1.4e-29, 1.19e-137j
0.015762882297770888737 + 3.1247278215310537576e-828j 1.21e-29, 1.02e-137j
0.0036085750055919218346 - 9.4080466593711754883e-828j 1.89e-30, 1.61e-138j
0.023516340499234959833 + 5.0529704542712961806e-827j 3.22e-31, 2.73e-139j
0.015762882297770888737 - 1.2411501512985612291e-826j 2.89e-31, 2.45e-139j
0.00075662304176886770601 - 4.3893897972397752457e-825j 6.03e-31, 5.12e-139j
0.023516340499234959833 - 2.8936393191122602492e-828j 3.21e-32, 2.73e-140j
0.052066193458757382163 - 1.932558035941516932e-827j 5.39e-34, 4.57e-142j
0.00075662304176886770601 - 2.971571793786998249e-828j 6.47e-32, 5.49e-140j
0.021024143600362087627 - 6.0317964415392670969e-827j 5.41e-32, 4.59e-140j
0.0054793513493940698995 - 2.3322614665013815309e-825j 7.6e-32, 6.45e-140j
0.018430100027595088746 - 2.7837391594607054598e-828j 2.11e-32, 1.79e-140j
0.029960366643982936496 + 6.438257299655067668e-828j 6.26e-34, 5.32e-142j
0.013053172036381860951 + 2.1609647762510635161e-826j 2.86e-32, 2.43e-140j
0.031474189759415731057 + 8.595689907013378598e-827j 5.57e-35, 4.73e-143j
0.025872788123951183919 - 4.7695635027279991726e-827j 1.12e-33, 9.54e-142j
0.007758768739348155559 - 6.7000482387492925688e-828j 1.08e-33, 9.21e-142j
0.031474189759415731057 - 1.0623112162130688536e-827j 6.64e-36, 5.64e-144j
0.021024143600362087627 + 2.7106062460088401773e-828j 7.15e-34, 6.07e-142j
0.028046224650759843065 + 5.0843003389888549836e-827j 3.44e-35, 2.92e-143j
0.029960366643982936496 - 6.1628187230464211912e-827j 1.08e-35, 9.13e-144j
0.049232699757499893639 + 1.5089037013574853245e-827j 5.44e-40, 4.62e-148j
0.025872788123951183919 + 3.3998105074085178887e-828j 7.51e-36, 6.38e-144j
0.031781070226768593936 - 4.4369928865211022942e-827j 3.72e-38, 3.16e-146j
0.018430100027595088746 + 8.1259835718181215091e-827j 2.22e-35, 1.88e-143j
0.028900232132361820561 - 5.624294861087720726e-826j 3e-39, 2.54e-147j
0.031781070226768593936 + 2.6782786433312309624e-826j 1.12e-38, 9.52e-147j
0.0020145241994806266316 + 7.6609999442535556473e-828j 4e-36, 3.4e-144j
0.024014213218449068719 + 2.8523823237886036281e-826j 2.76e-41, 2.34e-149j
0.010349359285983692256 + 4.9840228268364960547e-828j 1.33e-36, 1.13e-144j
0.007758768739348155559 + 9.5646054502176792522e-826j 2.32e-38, 1.97e-146j
0.024579345950605695539 + 1.0231960018035658144e-825j 4.37e-41, 3.71e-149j
0.032294509212933535043 + 2.0191632851393785695e-827j 9.22e-40, 7.83e-148j
0.028900232132361820561 + 1.0508817875844342871e-826j 6.08e-41, 5.16e-149j
0.024579345950605695539 - 2.1074160400166844497e-826j 1.98e-41, 1.68e-149j
0.032294509212933535043 - 1.4005958407503645549e-826j 5.09e-41, 4.32e-149j
0.032163932849509133606 - 7.6560557583207770769e-826j 1.11e-44, 9.41e-153j
0.010349359285983692256 - 4.2907079596784814037e-826j 7.23e-40, 6.14e-148j
0.028046224650759843065 - 4.4240906124007936401e-828j 3.22e-40, 2.73e-148j
0.033863638447727646879 - 1.5792924062695687191e-826j 3.45e-45, 2.93e-153j
0.0054793513493940698995 + 8.5641393210345394753e-828j 1.62e-38, 1.38e-146j
0.024014213218449068719 - 1.2758684152290989132e-825j 5.78e-44, 4.9e-152j
0.028122713664422440094 + 1.0889816328924042641e-825j 1.07e-44, 9.06e-153j
0.0036085750055919218346 + 6.7223484799768841087e-825j 5.32e-41, 4.51e-149j
0.032163932849509133606 + 2.0455924153713624233e-826j 1.89e-45, 1.61e-153j
0.028122713664422440094 - 2.6490027185798139408e-826j 1.31e-44, 1.11e-152j
0.042380200880159002577 + 8.9315215377666087477e-827j 9.15e-51, 7.77e-159j
0.036280207564007194531 + 2.503844427362752412e-826j 6.6e-50, 5.6e-158j
0.045252404874119898506 - 5.3781888417047211451e-827j 1.83e-51, 1.55e-159j
0.034658904813477553599 + 1.2233092670468102005e-826j 3.42e-49, 2.9e-157j
0.036280207564007194531 - 8.903986949615859481e-827j 2.67e-50, 2.26e-158j
0.026276815094629456832 - 1.109680036490457565e-824j 7.86e-55, 6.67e-163j
0.033863638447727646879 + 5.363756619034507369e-826j 4.19e-50, 3.54e-158j
0.034658904813477553599 - 3.7775847175031953876e-826j 8.84e-51, 7.48e-159j
0.052432598989438172318 - 4.0372522669323770601e-827j 4.58e-56, 3.87e-164j
0.039129182354293294022 + 5.9695257472608328858e-827j 1.75e-53, 1.48e-161j
0.047516699061321309368 - 1.8642104126886135365e-827j 2.08e-55, 1.76e-163j
0.052066193458757382163 + 2.3857952266152362953e-827j 7.49e-57, 6.33e-165j
0.039129182354293294022 - 1.5261424752429439685e-826j 4.97e-54, 4.21e-162j
0.051436471937020227861 - 2.03360931927018992e-827j 2.23e-57, 1.89e-165j
0.051436471937020227861 + 1.482265474079114409e-827j 2.65e-57, 2.24e-165j
0.042380200880159002577 - 3.8567628663791845951e-827j 5.47e-56, 4.63e-164j
0.052432598989438172318 + 3.6337600559871240372e-827j 2.99e-57, 2.53e-165j
0.047516699061321309368 + 3.5111047583440351157e-827j 1.49e-57, 1.26e-165j
0.049232699757499893639 - 2.5575957048341673441e-827j 3.59e-58, 3.04e-166j
0.026276815094629456832 + 1.1098741573569633602e-824j 1.25e-55, 1.08e-163j
0.045252404874119898506 + 2.5724660891599814015e-827j 2.31e-58, 1.99e-166j
0.05051055625147676589 - 1.3877340359585019958e-827j 7.33e-59, 6.39e-167j
0.05051055625147676589 + 2.1162004524667492885e-827j 6.21e-59, 5.01e-167j

Download

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