Rule: Q[2, 46, 49]

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)
-0.99979620672598640398 - 4.150332944728714094e-1689j 1e-475, 1e-475j
-0.95301649109280413346 - 1.0097862222456826927e-1692j 7.03e-476, 7.03e-476j
-0.94271837510039035867 - 7.3701427867691793314e-1693j 3.67e-476, 3.67e-476j
0.98934557770794047188 + 1.4881916757960320512e-1689j 4.34e-475, 4.34e-475j
0.95301649109280413346 + 1.6078661667305574107e-1702j 6.8e-476, 6.8e-476j
0.93142727437917378807 + 1.3750101019688295006e-1713j 1.84e-476, 1.84e-476j
-0.96231460512957343527 + 3.7296659382768033931e-1718j 1.2e-475, 1.2e-475j
-0.90593252997857285282 - 1.2179596587633865007e-1726j 3.54e-477, 3.54e-477j
-0.86060359194123489119 + 7.8780406355162406724e-1728j 1.5e-478, 1.5e-478j
0.99668949706175455644 + 2.4986440965727690558e-1721j 4.1e-475, 4.1e-475j
0.89175459604961934246 + 1.653189886799856799e-1742j 1.34e-477, 1.34e-477j
0.94271837510039035867 - 6.0512972834708609983e-1740j 3.85e-476, 3.85e-476j
-0.93142727437917378807 + 3.0893165883257035714e-1749j 1.74e-476, 1.74e-476j
-0.89175459604961934246 + 2.3239067777267816359e-1750j 1.26e-477, 1.26e-477j
-0.99877181556781104255 - 2.2869003672638898169e-1746j 2.8e-475, 2.8e-475j
0.8436680578134902362 + 2.2985848588573738654e-1755j 4.62e-479, 4.62e-479j
0.86060359194123489119 + 2.0409170652382903999e-1754j 1.54e-478, 1.54e-478j
0.96231460512957343527 - 1.2692974766980345647e-1754j 1.18e-475, 1.18e-475j
-0.76726238753913197782 + 5.4239871351738297342e-1777j 1.7e-481, 1.7e-481j
-0.91916007238168184229 + 4.064731065429329627e-1772j 8.4e-477, 8.4e-477j
0.87663867909948142213 - 2.1103345891365257614e-1769j 4.83e-478, 4.83e-478j
0.76726238753913197782 - 1.0675350412900655877e-1780j 1.71e-481, 1.71e-481j
-0.57735026918962576451 - 7.2026561228112748737e-1787j 4.78e-488, 4.78e-488j
-0.8436680578134902362 + 1.7456110534730038427e-1777j 4.54e-479, 4.54e-479j
-0.82584734035569671922 + 1.6272500582093526604e-1777j 1.3e-479, 1.3e-479j
-0.99668949706175455644 - 2.1435026686570900749e-1771j 3.7e-475, 3.7e-475j
0.7241468119421452457 + 3.1968097991217483477e-1790j 6.32e-483, 6.32e-483j
0.80715842173132252386 + 7.0060450712371165785e-1789j 3.27e-480, 3.27e-480j
0.99353439340965969908 - 1.4082937943406169882e-1793j 4.73e-475, 4.73e-475j
-0.65383545741169409993 + 7.3586594859142210358e-1843j 2.53e-485, 2.53e-485j
0.99979620672598640398 + 6.2069107109007395922e-1830j 1.05e-475, 1.05e-475j
0.82584734035569671922 - 1.1346293761288000627e-1858j 1.21e-479, 1.21e-479j
0.67799210954687477545 - 2.136272986883641474e-1864j 1.82e-484, 1.82e-484j
-0.9841347920523122598 + 9.8843381959649233472e-1852j 3.88e-475, 3.88e-475j
-0.74609672268758600303 - 3.2764458556371182889e-1873j 3.62e-482, 3.62e-482j
-0.78762283367173715749 - 2.949234693917763264e-1872j 8e-481, 8e-481j
0.9841347920523122598 + 1.9650268590168190673e-1864j 3.74e-475, 3.74e-475j
0.65383545741169409993 + 4.4620492023056050325e-1889j 2.72e-485, 2.72e-485j
0.90593252997857285282 - 3.8857204677825075407e-1878j 3.25e-477, 3.25e-477j
-0.46702179076295320509 + 1.0586705146094461459e-1898j 3.97e-492, 3.97e-492j
-0.60348729964043259864 + 4.4879039339449091893e-1894j 4.28e-487, 4.28e-487j
0.91916007238168184229 + 1.3874725552515765276e-1881j 7.57e-477, 7.57e-477j
0.78762283367173715749 + 4.1605584426516080124e-1888j 8.28e-481, 8.28e-481j
0.62899151175787332056 + 2.2278165585905325988e-1893j 3.62e-486, 3.62e-486j
-0.99353439340965969908 - 3.4355037889724990436e-1880j 4.6e-475, 4.6e-475j
-0.62899151175787332056 - 3.1173453701660630731e-1900j 3.5e-486, 3.5e-486j
-0.7241468119421452457 - 1.2957078576517829152e-1896j 6.91e-483, 6.91e-483j
0.19315479588911359251 + 2.1062247791474185799e-1917j 5.13e-503, 5.13e-503j
0.49541315992799992694 + 1.0155339107176538606e-1904j 4.71e-491, 4.71e-491j
0.74609672268758600303 - 4.5293194445909949156e-1896j 3.46e-482, 3.46e-482j
-0.31831919635271208942 + 7.5522175312632642437e-1912j 6.24e-498, 6.24e-498j
-0.55060696211465863102 - 1.2619192260056776763e-1902j 5.42e-489, 5.42e-489j
0.99877181556781104255 + 4.6581276153254328912e-1887j 2.8e-475, 2.8e-475j
0.60348729964043259864 + 1.0507845248848363175e-1909j 4.38e-487, 4.38e-487j
0.52328480048038451693 + 7.3072321593028723074e-1912j 5.14e-490, 5.14e-490j
-0.87663867909948142213 - 2.0735580585717861815e-1899j 4.93e-478, 4.93e-478j
-0.52328480048038451693 - 2.7720411282687952411e-1912j 5.29e-490, 5.29e-490j
-0.98934557770794047188 - 2.2335124109091387877e-1894j 4.2e-475, 4.2e-475j
-0.97788956408719486938 + 1.0542424114048704861e-1897j 2.83e-475, 2.83e-475j
0.40879724340009108784 - 9.2152381207575756863e-1919j 2.43e-494, 2.43e-494j
0.97788956408719486938 - 7.525748462846731063e-1901j 2.82e-475, 2.82e-475j
-0.9706101082582881573 + 2.0321210031117059995e-1914j 1.93e-475, 1.93e-475j
-0.43813986090857598555 + 3.3360277443075369409e-1934j 3.18e-493, 3.18e-493j
0.9706101082582881573 + 2.8255116431640530515e-1926j 1.82e-475, 1.82e-475j
0.46702179076295320509 - 5.317716394854961366e-1947j 4.16e-492, 4.16e-492j
0.57735026918962576451 + 6.8072229163246766994e-1944j 4.75e-488, 4.75e-488j
-0.80715842173132252386 + 7.139326733717696783e-1941j 3.25e-480, 3.25e-480j
-0.37902525146912541911 - 2.8698293094017081353e-1956j 1.55e-495, 1.55e-495j
-0.70143701791633045079 - 4.6819174715423329426e-1942j 1.12e-483, 1.12e-483j
0.70143701791633045079 + 1.3060366836619743285e-1945j 1.11e-483, 1.11e-483j
0.34885548892634643684 - 3.4977290776644974982e-1959j 9.94e-497, 9.94e-497j
-0.67799210954687477545 + 6.5458600366200052313e-1956j 1.9e-484, 1.9e-484j
-0.40879724340009108784 + 6.9709283435735311834e-1967j 2.33e-494, 2.33e-494j
-0.34885548892634643684 + 4.1449269025076588204e-1969j 9.63e-497, 9.63e-497j
0.55060696211465863102 + 1.5538229657426245576e-1965j 5.23e-489, 5.23e-489j
0.37902525146912541911 + 3.5448668352455141972e-1971j 1.56e-495, 1.56e-495j
0.43813986090857598555 + 5.6917607210978440024e-1969j 3.35e-493, 3.35e-493j
-0.097035890520288195344 - 1.1608805558067760172e-1982j 5.26e-507, 5.26e-507j
-0.28744815544929540845 - 5.6989272019624310569e-1974j 3.66e-499, 3.66e-499j
-0.49541315992799992694 - 2.073911385794710987e-1967j 4.57e-491, 4.57e-491j
0.31831919635271208942 + 1.6985354416016753177e-1974j 6.27e-498, 6.27e-498j
0.28744815544929540845 - 1.4846391474601857141e-1975j 3.6e-499, 3.6e-499j
0.097035890520288195344 + 4.067635941204257486e-1983j 4.97e-507, 4.97e-507j
-0.16127334095055363432 + 1.4579290121765390976e-1980j 2.46e-504, 2.46e-504j
-0.19315479588911359251 - 5.0214006571425093449e-1979j 4.94e-503, 4.94e-503j
0.064747330020785520411 + 1.0287168609183929135e-1984j 2.44e-508, 2.44e-508j
0.25627513995453353926 + 1.451243763535036896e-1976j 1.9e-500, 1.9e-500j
0.16127334095055363432 - 5.1910893223975779931e-1981j 2.52e-504, 2.52e-504j
-0.032390669202207414221 - 1.4649274038038464449e-1985j 1.33e-509, 1.33e-509j
-0.25627513995453353926 - 1.3370812364071056843e-1976j 2.16e-500, 2.16e-500j
-0.064747330020785520411 - 1.0633084694624242457e-1984j 2.33e-508, 2.33e-508j
0.12922245068283986911 + 8.3439707694607540299e-1982j 1.1e-505, 1.1e-505j
0.22483310504694234936 - 8.6281336166992495027e-1978j 1.02e-501, 1.02e-501j
0.032390669202207414221 - 4.0177481588095553891e-1986j 1.33e-509, 1.33e-509j
-0.22483310504694234936 - 7.0500563523195794532e-1978j 1.1e-501, 1.1e-501j
-0.12922245068283986911 - 9.9133900700719468917e-1982j 1.1e-505, 1.1e-505j
-6.7091299999953323333e-2238 - 3.7938745844542031745e-2238j 7.48e-2236, 7.48e-2236j

Weights

Weight (ball center) Error (ball radius)
0.00054904771224758026878 - 4.4083683902215017171e-1689j 2.21e-112, 4.54e-341j
0.0097983538665269374815 + 8.7424690043620836306e-1690j 1.1e-112, 2.25e-341j
0.010796815517479754535 - 7.8954741454912360934e-1690j 6.73e-113, 1.38e-341j
0.0046985154589285839611 - 1.8246888038086258638e-1690j 6.24e-114, 1.28e-342j
0.0097983538665269374815 + 4.2159200289709057473e-1690j 3.8e-114, 7.79e-343j
0.011782306969220694693 + 3.2670036684024488577e-1690j 2.64e-114, 5.42e-343j
0.0087978044907986944609 - 9.7919723031910876387e-1690j 2.47e-113, 5.07e-342j
0.01370425495895533333 + 6.1338723730278473064e-1690j 2.7e-114, 5.53e-343j
0.016488069127712188202 - 5.0068984838561396815e-1690j 2.92e-115, 5.99e-344j
0.002625123060322554201 + 5.2675634551022553096e-1690j 3.19e-117, 6.55e-346j
0.014649629032323789301 - 2.5401403259623048115e-1690j 6.34e-117, 1.3e-345j
0.010796815517479754535 - 3.6658753190047499023e-1690j 5.61e-116, 1.15e-344j
0.011782306969220694693 + 7.2114599184991813392e-1690j 3.2e-114, 6.57e-343j
0.014649629032323789301 - 5.7056392337390282408e-1690j 6.92e-115, 1.42e-343j
0.0015385932790055359268 + 6.5345943083110825118e-1689j 4.87e-116, 9.99e-345j
0.017380581770205568155 + 2.1484739842903208262e-1690j 2.38e-118, 4.87e-347j
0.016488069127712188202 - 2.2561884745808396966e-1690j 3.89e-118, 7.99e-347j
0.0087978044907986944609 - 5.0210622030376427045e-1690j 4.26e-118, 8.73e-347j
0.020766277674347474942 + 3.8318873859709979692e-1690j 2.73e-120, 5.61e-349j
0.012749372867962862297 - 6.6287043406380822011e-1690j 2.04e-116, 4.19e-345j
0.015578911350019058991 + 2.3846236509450135478e-1690j 3.87e-118, 7.93e-347j
0.020766277674347474942 + 1.8558254367618776358e-1690j 2.83e-121, 5.81e-350j
0.026444581248344181124 + 2.7894667641940927089e-1690j 8.86e-123, 1.82e-351j
0.017380581770205568155 + 4.7182539533983838964e-1690j 4.61e-119, 9.46e-348j
0.018258085260636177544 - 4.4601301575870620477e-1690j 9.68e-120, 1.99e-348j
0.002625123060322554201 - 3.5082610008530567829e-1689j 1.01e-119, 2.08e-348j
0.022334085522638365135 + 1.7646145918061011575e-1690j 9.72e-124, 1.99e-352j
0.019116059178763386486 + 1.9790989912071390851e-1690j 4.12e-122, 8.45e-351j
0.0036773113448485397082 - 1.2879269823880445688e-1689j 9.97e-123, 2.04e-351j
0.024504614517768477947 - 3.104347478763567755e-1690j 2.02e-126, 4.14e-355j
0.00054904771224758026878 + 7.7098416440707363648e-1691j 1.27e-123, 2.61e-352j
0.018258085260636177544 - 2.0569883612571987857e-1690j 1.17e-122, 2.4e-351j
0.023804648595304092852 + 1.6979481915590408717e-1690j 9.42e-127, 1.93e-355j
0.0057259736612415546447 + 1.5250892408079942301e-1689j 3.84e-124, 7.87e-353j
0.02156160269095871022 - 3.6598472078349546788e-1690j 5.34e-126, 1.09e-354j
0.019951427296771266821 - 4.0204993633507187325e-1690j 4.89e-125, 1e-353j
0.0057259736612415546447 + 1.6519550584419263597e-1689j 5.37e-124, 1.1e-352j
0.024504614517768477947 - 1.6718147133438132041e-1690j 1e-128, 2.06e-357j
0.01370425495895533333 + 2.7303143280969372731e-1690j 5.96e-124, 1.22e-352j
0.02864150943766805692 + 2.4619661433267256925e-1690j 1.91e-132, 3.91e-361j
0.025825100115079886324 - 2.8866728872227357262e-1690j 5.49e-130, 1.13e-358j
0.012749372867962862297 - 2.9660825067624021549e-1690j 3.68e-124, 7.55e-353j
0.019951427296771266821 - 1.912741189747368562e-1690j 2.45e-126, 5.03e-355j
0.02517871964248669551 + 1.6498620684536016027e-1690j 8.65e-131, 1.77e-359j
0.0036773113448485397082 + 2.4180485061485622931e-1689j 4.73e-128, 9.7e-357j
0.02517871964248669551 + 2.9913071065123203289e-1690j 4.76e-131, 9.76e-360j
0.022334085522638365135 + 3.5026753311725054143e-1690j 5.64e-130, 1.16e-358j
0.031785463816484930743 - 1.6491241883609929953e-1690j 2.26e-138, 4.63e-367j
0.028136399520321329164 - 1.5905864497592455328e-1690j 5.07e-136, 1.04e-364j
0.02156160269095871022 - 1.8067538815382375267e-1690j 1.08e-129, 2.22e-358j
0.030709059576278658677 - 2.157379547059014132e-1690j 2.11e-138, 4.33e-367j
0.027037486939550072653 - 2.6988724960129408978e-1690j 2.68e-134, 5.49e-363j
0.0015385932790055359268 - 2.5141168403182135795e-1690j 1.61e-128, 3.3e-357j
0.025825100115079886324 - 1.6317585930138816481e-1690j 1.08e-133, 2.2e-362j
0.027601901823742293686 + 1.5966399520953626829e-1690j 6.13e-136, 1.26e-364j
0.015578911350019058991 + 5.3329436196002188763e-1690j 2.07e-130, 4.25e-359j
0.027601901823742293686 + 2.6144080359695571083e-1690j 2.62e-135, 5.37e-364j
0.0046985154589285839611 - 1.868295774873022774e-1689j 3.4e-131, 6.96e-360j
0.0067644992234512819321 - 1.2850305790346986333e-1689j 1.06e-131, 2.17e-360j
0.02956259992272690612 + 1.5866986324236463707e-1690j 3.19e-141, 6.54e-370j
0.0067644992234512819321 - 8.9227895304332783764e-1690j 4.38e-132, 8.98e-361j
0.0077908539699748069251 + 1.1103011443756595763e-1689j 4.78e-132, 9.8e-361j
0.029117388110578970041 - 2.392942785792877916e-1690j 5.58e-141, 1.14e-369j
0.0077908539699748069251 + 6.3353220656341837256e-1690j 3.73e-132, 7.64e-361j
0.02864150943766805692 + 1.5870198316708905417e-1690j 3.67e-141, 7.52e-370j
0.026444581248344181124 + 1.6170627883732596317e-1690j 5.44e-139, 1.12e-367j
0.019116059178763386486 + 4.2286534416201038978e-1690j 4.16e-135, 8.54e-364j
0.029976102246867085342 - 2.2676695312022065595e-1690j 2.21e-143, 4.54e-372j
0.023081333955059353037 - 3.3588591040308500486e-1690j 2.15e-137, 4.41e-366j
0.023081333955059353037 - 1.7286437124943364531e-1690j 2.18e-137, 4.47e-366j
0.030358238740833642714 + 1.5949357276322345024e-1690j 1.72e-145, 3.54e-374j
0.023804648595304092852 + 3.2265774519998327108e-1690j 6.52e-138, 1.34e-366j
0.02956259992272690612 + 2.3282677374176726443e-1690j 3.03e-143, 6.22e-372j
0.030358238740833642714 + 2.2108047035431989127e-1690j 7.49e-145, 1.54e-373j
0.027037486939550072653 - 1.6054142442471057545e-1690j 2.54e-141, 5.21e-370j
0.029976102246867085342 - 1.5898015436880405604e-1690j 1.64e-145, 3.37e-374j
0.029117388110578970041 - 1.5857491135676629674e-1690j 5.26e-144, 1.08e-372j
0.032243181744741162602 + 1.8647246352905844166e-1690j 1.43e-151, 2.93e-380j
0.031027540056184237078 + 2.1072101448786402957e-1690j 3.63e-148, 7.44e-377j
0.028136399520321329164 - 2.5356278864524078122e-1690j 1.09e-143, 2.23e-372j
0.030709059576278658677 - 1.6020053986247970981e-1690j 2.4e-148, 4.91e-377j
0.031027540056184237078 + 1.610988372979711231e-1690j 2.03e-149, 4.16e-378j
0.032243181744741162602 + 1.7037249196083977167e-1690j 4.13e-153, 8.48e-382j
0.031971814615748987548 + 1.9354136554367805935e-1690j 9.18e-153, 1.88e-381j
0.031785463816484930743 - 1.974375161844028554e-1690j 1.89e-152, 3.87e-381j
0.032328287888843523624 - 1.7256274442466451608e-1690j 4.57e-154, 9.38e-383j
0.031312990127026878816 - 1.6218671349739375795e-1690j 4.43e-152, 9.1e-381j
0.031971814615748987548 + 1.6654829846068511375e-1690j 1.74e-153, 3.57e-382j
0.032379344757431184872 + 1.8029408467335882312e-1690j 2.35e-155, 4.83e-384j
0.031312990127026878816 - 2.060122786728139673e-1690j 5.69e-154, 1.17e-382j
0.032328287888843523624 - 1.8327620522691260372e-1690j 3.02e-155, 6.2e-384j
0.032124335731887152823 - 1.6836827529626416424e-1690j 7.17e-155, 1.47e-383j
0.031565637319509784328 + 1.6345899754085805029e-1690j 2.18e-154, 4.49e-383j
0.032379344757431184872 + 1.7494329787120140261e-1690j 5.44e-156, 1.12e-384j
0.031565637319509784328 + 2.0159048582004276467e-1690j 4.56e-156, 9.54e-385j
0.032124335731887152823 - 1.8989063142931211991e-1690j 1.94e-156, 4.11e-385j
0.032396328528383510582 - 1.7751872143583080019e-1690j 1.92e-156, 3.88e-385j

Download

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