Rule: Q[1, 10, 24, 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)
-0.99691005464477308316 - 1.261919589920471031e-827j 4.15e-228, 4.15e-228j
-0.96795145857685108262 + 1.7684628674475155389e-837j 3.79e-229, 3.79e-229j
-0.925196002776519573 + 1.2448692635680998395e-843j 2.52e-230, 2.52e-230j
-0.99914652732514104357 + 3.3962755795476171394e-844j 6.71e-228, 6.71e-228j
0.925196002776519573 + 7.0759062177458536048e-862j 3.05e-230, 3.05e-230j
0.94140719606100902773 - 4.5960750656485701425e-862j 6.73e-230, 6.73e-230j
0.9782286581460569928 + 2.9105260252580766754e-859j 7.94e-229, 7.94e-229j
-0.94140719606100902773 - 5.5004022541061871072e-862j 7e-230, 7e-230j
0.78913679525560244035 + 6.3767667446998435653e-868j 1.11e-233, 1.11e-233j
-0.99269927422948553157 + 1.5848371226964857243e-859j 2.42e-228, 2.42e-228j
0.86521950084221596032 - 3.3709849870232723096e-873j 9.18e-232, 9.18e-232j
0.99914652732514104357 + 9.429791407034515259e-868j 6.32e-228, 6.32e-228j
-0.90706861264267571612 + 2.3782654909767940535e-873j 1.07e-230, 1.07e-230j
-0.86521950084221596032 - 2.2898312457909976748e-878j 8.92e-232, 8.92e-232j
0.99691005464477308316 + 4.2010084899228092045e-876j 4.19e-228, 4.19e-228j
0.84158444565058652392 - 7.4692581226314047701e-883j 2.49e-232, 2.49e-232j
0.90706861264267571612 + 4.8457050974968038543e-881j 9.42e-231, 9.42e-231j
0.18094636520965929953 - 2.8684948423577909575e-900j 2.19e-250, 2.19e-250j
-0.78913679525560244035 + 2.1277599158841823686e-882j 1.22e-233, 1.22e-233j
-0.95566886457188528153 + 3.9695731786364470074e-876j 1.77e-229, 1.77e-229j
0.96795145857685108262 + 6.0100836444746259194e-889j 3.75e-229, 3.75e-229j
0.76043234423651846217 + 1.8508052688685307902e-893j 2.17e-234, 2.17e-234j
-0.99978541389155894061 + 2.1001145133443847121e-883j 4.09e-228, 4.09e-228j
-0.84158444565058652392 + 8.3464738946573845427e-904j 2.37e-232, 2.37e-232j
-0.81620611180145403617 - 1.6592161935508972595e-904j 5.2e-233, 5.2e-233j
0.99978541389155894061 + 8.8823173451258933443e-898j 4e-228, 4e-228j
0.69835832010768922539 - 2.9999312362801179927e-910j 5.69e-236, 5.69e-236j
0.81620611180145403617 - 1.9596842601963796887e-907j 5.49e-233, 5.49e-233j
0.95566886457188528153 + 4.6716329832113043037e-903j 1.72e-229, 1.72e-229j
-0.63049706440579439658 - 2.3123896079592424855e-910j 9.82e-238, 9.82e-238j
-0.88706259976809529908 - 4.9077222925901868612e-900j 3.16e-231, 3.16e-231j
-0.9782286581460569928 + 3.6901448188134820384e-907j 7.97e-229, 7.97e-229j
0.73015200557404932409 + 2.3601613516150799261e-930j 3.82e-235, 3.82e-235j
0.98647982832670103524 + 6.5791777622330653845e-922j 1.38e-228, 1.38e-228j
-0.69835832010768922539 - 4.3057000715393872556e-932j 6.06e-236, 6.06e-236j
-0.76043234423651846217 - 2.6141115852799065638e-931j 2.12e-234, 2.12e-234j
0.66511705212951455584 + 4.0521010278264204433e-935j 7.93e-237, 7.93e-237j
0.59457013709158187507 - 2.4197492214650643358e-938j 1.21e-238, 1.21e-238j
0.99269927422948553157 + 2.2373264511474226586e-929j 2.55e-228, 2.55e-228j
-0.73015200557404932409 + 3.1098868465823181646e-934j 3.79e-235, 3.79e-235j
-0.59457013709158187507 - 1.7171049966608938451e-938j 1.12e-238, 1.12e-238j
-0.98647982832670103524 - 8.425780985893557783e-940j 1.38e-228, 1.38e-228j
0.55741079119411217762 - 6.3449161360255205132e-958j 1.24e-239, 1.24e-239j
0.63049706440579439658 + 2.568963192849951567e-956j 1.09e-237, 1.09e-237j
-0.13603911584880836045 + 6.7567576115298963027e-971j 1.06e-251, 1.06e-251j
-0.55741079119411217762 - 4.595905558199285952e-959j 1.2e-239, 1.2e-239j
-0.66511705212951455584 + 3.1801453011993818331e-956j 8.05e-237, 8.05e-237j
0.88706259976809529908 + 7.3626104811018740695e-966j 3.29e-231, 3.29e-231j
0.47970565823322191124 - 3.3456106729661350922e-973j 9.96e-242, 9.96e-242j
0.51909612920681181593 + 2.2626680601021844571e-974j 1.1e-240, 1.1e-240j
-0.39802615560766787178 - 1.5430281460033001505e-976j 4.95e-244, 4.95e-244j
-0.51909612920681181593 + 2.6848780789974588671e-974j 1.11e-240, 1.11e-240j
-0.18094636520965929953 - 2.7238535891463585453e-985j 2.17e-250, 2.17e-250j
0.22547846494321340121 - 1.8024410129761242217e-983j 4.94e-249, 4.94e-249j
0.43932109076235962814 - 4.7312062731158998633e-977j 7.13e-243, 7.13e-243j
1.6804649193868523337e-1027 - 1.830505684796512537e-1027j 1.76e-1025, 1.76e-1025j
-0.47970565823322191124 - 7.8678757555752786771e-976j 9.61e-242, 9.61e-242j
-0.43932109076235962814 - 3.0979874028546278899e-978j 7.66e-243, 7.66e-243j
0.045472046861558262908 + 2.2208697612234104182e-988j 2.19e-254, 2.19e-254j
0.39802615560766787178 - 1.8620188672696992289e-978j 4.92e-244, 4.92e-244j
0.090849783728614288704 - 1.5791572442713244336e-987j 4.66e-253, 4.66e-253j
-0.22547846494321340121 - 1.48718977965316735e-985j 5.38e-249, 5.38e-249j
-0.35590643072768674405 + 2.4988155357299656363e-979j 3.15e-245, 3.15e-245j
-0.045472046861558262908 - 1.7423122780800839812e-988j 2.34e-254, 2.34e-254j
0.35590643072768674405 - 1.0247591332141870208e-979j 3.31e-245, 3.31e-245j
0.26954315595234497233 + 1.7026320188921370426e-981j 1.05e-247, 1.05e-247j
-0.090849783728614288704 - 3.1051849971527876355e-987j 4.57e-253, 4.57e-253j
-0.31304917612197294573 - 5.9932367628045705458e-981j 1.81e-246, 1.81e-246j
-0.26954315595234497233 + 1.66488787469726211e-982j 1.02e-247, 1.02e-247j
0.13603911584880836045 - 1.5110835295167872259e-985j 1.16e-251, 1.16e-251j
0.31304917612197294573 - 5.7297265264223722297e-981j 1.79e-246, 1.79e-246j

Weights

Weight (ball center) Error (ball radius)
0.0032213866406494770426 + 8.5406047139443826673e-828j 6.74e-30, 2.84e-135j
0.011283982916780146662 - 5.2438203050209563217e-829j 2.39e-30, 1.01e-135j
0.017175200201971728725 + 1.4245321806255212893e-829j 1.1e-30, 4.63e-136j
0.001248705999265932216 - 2.5406750649326365234e-827j 2.29e-30, 9.65e-136j
0.017175200201971728725 + 5.3149499416960533874e-831j 7.01e-32, 2.96e-137j
0.015241640477360353289 - 5.9071522413116026496e-831j 5.28e-32, 2.23e-137j
0.0092668241998086235076 + 9.1979401337014125091e-831j 5.31e-33, 2.24e-138j
0.015241640477360353289 - 2.0629451109103796932e-829j 3.47e-31, 1.46e-136j
0.027896479899364184676 + 3.5738429652941007098e-831j 2.85e-33, 1.2e-138j
0.0052084210462128320348 + 6.9516395129057472608e-828j 4.61e-31, 1.94e-136j
0.022746891185178665557 - 4.1831075162604255772e-831j 7.88e-33, 3.33e-138j
0.001248705999265932216 + 2.8466880231243895196e-830j 2.15e-34, 9.08e-140j
0.019073310615243754669 - 1.0281325785770487007e-829j 7.96e-33, 3.36e-138j
0.022746891185178665557 - 5.9149938337743737439e-830j 5.55e-34, 2.34e-139j
0.0032213866406494770426 - 2.0388654343402236256e-830j 1.91e-34, 8.05e-140j
0.024515108197987883317 + 3.9392488510797065706e-831j 1.32e-34, 5.56e-140j
0.019073310615243754669 - 4.851362836756584455e-831j 4.74e-34, 2e-139j
0.044735124942217271002 + 3.399290374804985013e-831j 6.44e-39, 2.72e-144j
0.027896479899364184676 + 3.072123423267942337e-830j 7.2e-37, 3.04e-142j
0.013276788706847511586 + 3.1636422939094258364e-829j 1.15e-33, 4.84e-139j
0.011283982916780146662 - 7.7284670045112108246e-831j 3.87e-35, 1.63e-140j
0.029502546019921215509 - 3.4380585452627970706e-831j 7.99e-37, 3.37e-142j
0.00039408034605179495548 + 1.1432834858203944013e-827j 4.22e-33, 1.78e-138j
0.024515108197987883317 + 4.66264860821968477e-830j 1.1e-36, 4.66e-142j
0.026232842143422694019 - 3.7514644353776133352e-830j 3.18e-37, 1.34e-142j
0.00039408034605179495548 - 1.6463956524465330139e-830j 5.07e-36, 2.14e-141j
0.03252870115860083789 - 3.2372642353107666391e-831j 2.52e-40, 1.06e-145j
0.026232842143422694019 - 3.7388912393488998913e-831j 7.65e-38, 3.23e-143j
0.013276788706847511586 + 6.6820537845275930224e-831j 1.45e-36, 6.12e-142j
0.035285654678988951981 - 1.3821385048082197723e-830j 2.92e-43, 1.23e-148j
0.02093178512125758194 + 7.6866556323184894998e-830j 1.12e-37, 4.74e-143j
0.0092668241998086235076 + 9.7247589091534287464e-829j 6.4e-37, 2.7e-142j
0.031047706956517383753 + 3.3270071822399391627e-831j 1.4e-40, 5.9e-146j
0.0072342864187224736863 - 1.1357836915411506692e-830j 1.45e-37, 6.1e-143j
0.03252870115860083789 - 1.8382179847990596475e-830j 5.19e-43, 2.19e-148j
0.029502546019921215509 - 2.5549325727236169681e-830j 1.83e-41, 7.7e-147j
0.033942354442938543179 + 3.166225879807608122e-831j 2.46e-43, 1.04e-148j
0.036555777254656351769 + 3.0727867557411534596e-831j 2.27e-45, 9.57e-151j
0.0052084210462128320348 + 1.4712349326420444781e-830j 1.19e-38, 5.02e-144j
0.031047706956517383753 + 2.1539923154138811444e-830j 4.91e-43, 2.07e-148j
0.036555777254656351769 + 1.2154596254213412094e-830j 2.12e-46, 8.96e-152j
0.0072342864187224736863 - 2.1597823661929182006e-828j 4.18e-39, 1.76e-144j
0.037750061189632460035 - 3.0477427514793557967e-831j 6.74e-47, 2.84e-152j
0.035285654678988951981 - 3.1119041854242275554e-831j 4.23e-45, 1.78e-150j
0.04506385932447798492 - 4.6172346153165094328e-831j 4.17e-52, 1.76e-157j
0.037750061189632460035 - 1.0778562070535991027e-830j 3.64e-48, 1.54e-153j
0.033942354442938543179 + 1.5860350272546378838e-830j 1.49e-45, 6.28e-151j
0.02093178512125758194 + 4.4818036829028122958e-831j 4.8e-43, 2.02e-148j
0.039901311846810303221 - 3.0368760462402046133e-831j 4.22e-50, 1.78e-155j
0.038866008167680777868 + 3.0359559806007821653e-831j 5.09e-49, 2.15e-154j
0.041721738978951679753 - 7.164207216828056213e-831j 3.66e-53, 1.54e-158j
0.038866008167680777868 + 9.6324694513683577781e-831j 6.8e-51, 2.87e-156j
0.044735124942217271002 + 4.9069291228195517757e-831j 9.44e-55, 3.98e-160j
0.044313694812572792709 - 3.3063903044226297247e-831j 7.29e-55, 3.08e-160j
0.040853865585823072373 + 3.050186629170468526e-831j 1.24e-52, 5.23e-158j
0.045487772523743955016 + 3.9501932081683566463e-831j 3.32e-56, 1.4e-161j
0.039901311846810303221 - 8.6702644424955628961e-831j 7.98e-53, 3.37e-158j
0.040853865585823072373 + 7.8566351195680404923e-831j 1.55e-53, 6.54e-159j
0.045440599234397027598 - 3.7817772030177969756e-831j 1.29e-56, 5.44e-162j
0.041721738978951679753 - 3.0757882117880173607e-831j 1.78e-55, 7.51e-161j
0.045299188709448283245 + 3.6352724874329228965e-831j 7.44e-57, 3.14e-162j
0.044313694812572792709 - 5.2392118799394333912e-831j 2.62e-57, 1.11e-162j
0.042503164425413805157 + 6.5715474252757769173e-831j 1.06e-56, 4.46e-162j
0.045440599234397027598 - 4.1432619214787889879e-831j 1.25e-57, 5.26e-163j
0.042503164425413805157 + 3.1137894607529372732e-831j 8.73e-58, 3.68e-163j
0.043800474050312299952 + 3.2284563638833429566e-831j 2.97e-58, 1.25e-163j
0.045299188709448283245 + 4.3642829735216618629e-831j 3.74e-58, 1.58e-163j
0.043196547842641342697 - 6.0617178535582352357e-831j 1.15e-58, 4.86e-164j
0.043800474050312299952 + 5.6212194073800377683e-831j 9.13e-59, 3.85e-164j
0.04506385932447798492 - 3.5084037320419909112e-831j 1.64e-59, 7.01e-165j
0.043196547842641342697 - 3.1645043597143373791e-831j 1.56e-59, 6.44e-165j

Download

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