Rule: Q[2, 4, 36, 42]

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)
-0.9872303873932104259 + 9.4578866294838290566e-1860j 9.16e-480, 9.16e-480j
-0.96326778093049967835 + 1.8890677973874116976e-1860j 2.82e-480, 2.82e-480j
-0.92704507371965201272 - 2.9156806045782994064e-1863j 2.85e-481, 2.85e-481j
-0.99210203675286631524 + 1.7697358795549528716e-1859j 1.18e-479, 1.18e-479j
0.94061932901805627254 - 6.167218467201257236e-1862j 6.35e-481, 6.35e-481j
0.95286079650633186726 - 3.493780017457668503e-1873j 1.53e-480, 1.53e-480j
0.99210203675286631524 - 1.4510522491479382667e-1902j 1.11e-479, 1.11e-479j
-0.91248695683407599658 + 1.272835641267253741e-1928j 1.2e-481, 1.2e-481j
-0.99987996372374842967 - 1.9961906609788261113e-1924j 2.3e-480, 2.3e-480j
0.99851105949928519129 - 1.6092363424628392531e-1952j 5.9e-480, 5.9e-480j
0.84025595811263113901 + 9.9680225566680290553e-1986j 1.19e-483, 1.19e-483j
0.99568077095266101509 + 5.2793199387738949419e-2001j 9.97e-480, 9.97e-480j
-0.94061932901805627254 - 3.5298479457345466955e-2031j 6.72e-481, 6.72e-481j
-0.87897669460789045246 - 4.5379682470694636583e-2038j 1.44e-482, 1.44e-482j
0.9872303873932104259 - 2.7602355889814813758e-2032j 9.12e-480, 9.12e-480j
0.87897669460789045246 + 3.3660759658488305522e-2055j 1.43e-482, 1.43e-482j
0.92704507371965201272 + 4.5010713677114468244e-2058j 2.98e-481, 2.98e-481j
0.99987996372374842967 - 4.7180313425311626329e-2061j 2.09e-480, 2.09e-480j
-0.77276917497315810654 - 2.0063136606968313411e-2077j 1.46e-485, 1.46e-485j
-0.95286079650633186726 - 9.1788822767364583864e-2072j 1.43e-480, 1.43e-480j
0.91248695683407599658 + 4.7048194241314748373e-2073j 1.19e-481, 1.19e-481j
0.77276917497315810654 - 1.0042543074411405271e-2077j 1.47e-485, 1.47e-485j
-0.99568077095266101509 + 3.7097308320950762548e-2069j 1.04e-479, 1.04e-479j
-0.81913418995380245057 + 2.7745643839383325185e-2077j 3.33e-484, 3.33e-484j
-0.84025595811263113901 - 6.6225452436722354157e-2077j 1.2e-483, 1.2e-483j
0.86011555459655667758 + 8.2287144543848728625e-2076j 4.31e-483, 4.31e-483j
0.74808679440977429644 + 1.8219802379781122501e-2078j 2.93e-486, 2.93e-486j
0.89655496525765430757 + 2.2075684220892482001e-2074j 4.28e-482, 4.28e-482j
-0.86011555459655667758 + 5.1487182429885064482e-2076j 4.21e-483, 4.21e-483j
-0.63815642272838958413 - 9.0800139874285073246e-2086j 1.62e-489, 1.62e-489j
-0.89655496525765430757 - 6.4006571667989583819e-2075j 4.47e-482, 4.47e-482j
0.69518496586957738843 + 2.6037598687904677393e-2082j 8.21e-488, 8.21e-488j
0.66704471333701735281 + 2.4737437230053662146e-2081j 1.21e-488, 1.21e-488j
-0.99851105949928519129 - 1.3983490285201079564e-2070j 6.06e-480, 6.06e-480j
-0.66704471333701735281 + 7.9191842608364732707e-2082j 1.22e-488, 1.22e-488j
-0.74808679440977429644 + 1.0347707683759480798e-2079j 2.94e-486, 2.94e-486j
0.98040567633242411892 - 2.4468552283946665369e-2070j 6.19e-480, 6.19e-480j
0.63815642272838958413 - 8.2080379015639168379e-2089j 1.62e-489, 1.62e-489j
0.72228999145644398535 - 1.3804428769621177985e-2085j 5.24e-487, 5.24e-487j
-0.98040567633242411892 - 1.6336209459071496203e-2076j 5.98e-480, 5.98e-480j
-0.54550062166219007651 + 5.3236494415983286593e-2091j 2.01e-492, 2.01e-492j
-0.97225394892401551313 + 1.9194712582329759412e-2078j 4.14e-480, 4.14e-480j
0.79654065260956471698 - 8.7793841345097460476e-2083j 6.76e-485, 6.76e-485j
0.60833224326372810088 + 2.2593341556131125971e-2089j 1.95e-490, 1.95e-490j
0.81913418995380245057 + 1.0001309483443042252e-2081j 2.96e-484, 2.96e-484j
-0.57735026918962576451 - 4.0635069339332034573e-2091j 2.06e-491, 2.06e-491j
-0.69518496586957738843 - 5.045617695584056099e-2088j 8.51e-488, 8.51e-488j
0.96326778093049967835 - 5.173133182342585427e-2081j 2.79e-480, 2.79e-480j
0.51314160997085617842 - 8.9612970109266395552e-2106j 2.07e-493, 2.07e-493j
0.97225394892401551313 + 3.1425404896468405326e-2101j 4.36e-480, 4.36e-480j
-0.60833224326372810088 + 1.2527027854000885328e-2111j 2.01e-490, 2.01e-490j
-0.48005966382599618486 + 8.2279192030496825836e-2117j 1.65e-494, 1.65e-494j
-0.79654065260956471698 - 1.2887519980548556062e-2109j 7.25e-485, 7.25e-485j
0.57735026918962576451 - 7.9239331576510034228e-2119j 2.11e-491, 2.11e-491j
0.54550062166219007651 + 5.6032574138390584772e-2120j 2.1e-492, 2.1e-492j
-0.72228999145644398535 + 4.4350586760074819974e-2127j 5.24e-487, 5.24e-487j
-0.51314160997085617842 - 1.636895141488854472e-2135j 1.9e-493, 1.9e-493j
-0.34074129269951861202 + 4.3639943636041573367e-2140j 4e-499, 4e-499j
0.48005966382599618486 + 1.2819391939105640882e-2136j 1.7e-494, 1.7e-494j
0.4111111626798532654 + 6.8844130411639220391e-2138j 9.25e-497, 9.25e-497j
0.15655801081562154215 - 3.2768716473028972577e-2149j 1.96e-505, 1.96e-505j
-0.4111111626798532654 + 4.7167127407441163103e-2137j 9.16e-497, 9.16e-497j
-0.4459311574120021154 - 2.2342348989641760284e-2136j 1.44e-495, 1.44e-495j
-0.020496697440753133861 - 4.614074354907049285e-2152j 3.45e-510, 3.45e-510j
0.37614791095545046364 - 1.0741003292229292133e-2139j 6.46e-498, 6.46e-498j
0.4459311574120021154 - 1.7826134489883479863e-2136j 1.36e-495, 1.36e-495j
-0.057118014114781146719 - 4.2261053030570034614e-2150j 9.05e-509, 9.05e-509j
-0.37614791095545046364 - 8.2272550131769718405e-2139j 6.15e-498, 6.15e-498j
-0.15655801081562154215 + 3.3285031888667227751e-2147j 1.78e-505, 1.78e-505j
0.1945790327703601808 - 5.0643954340488041778e-2146j 3.87e-504, 3.87e-504j
0.34074129269951861202 + 1.8788082108267239477e-2141j 3.88e-499, 3.88e-499j
0.08327020363365321691 + 1.04313437085370147e-2149j 8.01e-508, 8.01e-508j
-0.26721627858316333241 - 5.7341772558416036058e-2143j 1.27e-501, 1.27e-501j
-0.23081009518813896127 + 1.3172989855135703298e-2143j 7.43e-503, 7.43e-503j
0.057118014114781146719 - 2.0699518551179465643e-2151j 9.7e-509, 9.7e-509j
0.26721627858316333241 + 1.582056733842063008e-2143j 1.35e-501, 1.35e-501j
0.23081009518813896127 + 1.3547015193196339541e-2145j 7.36e-503, 7.36e-503j
-0.11732817022260797665 - 1.5149765050405502884e-2148j 9e-507, 9e-507j
-0.3042598527464201821 - 2.0431729752150974668e-2141j 2.4e-500, 2.4e-500j
-0.08327020363365321691 + 3.9154721913627366428e-2149j 8.56e-508, 8.56e-508j
0.11732817022260797665 + 4.701390355134150195e-2149j 9.58e-507, 9.58e-507j
0.3042598527464201821 + 6.5259707840655550715e-2142j 2.39e-500, 2.39e-500j
0.020496697440753133861 + 3.443313385275855235e-2152j 3e-510, 3e-510j
-0.1945790327703601808 + 2.3169387216429887567e-2145j 4.26e-504, 4.26e-504j

Weights

Weight (ball center) Error (ball radius)
0.0058914912367405302368 - 1.6629335469750130064e-1859j 1.43e-125, 2.47e-357j
0.0095377965370229202187 + 2.6881451285811578674e-1861j 7.03e-126, 1.21e-357j
0.014057896901788855947 - 7.7863548522788583716e-1861j 3.39e-126, 5.84e-358j
0.0039844889005139931593 + 1.068854319226639937e-1859j 3.38e-126, 5.82e-358j
0.013018060697863549775 - 2.4244678148368270641e-1862j 1.96e-127, 3.37e-359j
0.011357677472371628183 + 8.8817487995395398854e-1862j 1.69e-127, 2.92e-359j
0.0039844889005139931593 - 2.8134617827731487385e-1862j 1.56e-128, 2.69e-360j
0.015145320484031285894 + 6.117913912207749987e-1861j 9.97e-128, 1.72e-359j
0.00051694860958528336367 + 6.4378360755723700801e-1861j 4.96e-128, 8.55e-360j
0.0022015550673638414115 - 9.8759347652067935964e-1863j 3.55e-129, 6.11e-361j
0.020418744012990465241 - 1.4766117670779617051e-1862j 3.82e-131, 6.59e-363j
0.0032962602749837408841 + 1.9219281674978235289e-1862j 4.85e-129, 8.35e-361j
0.013018060697863549775 + 1.0877485728190778087e-1860j 6.41e-129, 1.1e-360j
0.018304663996866639456 + 3.8948715721407988422e-1861j 1.84e-130, 3.17e-362j
0.0058914912367405302368 + 3.1479816965265030547e-1862j 1.37e-129, 2.36e-361j
0.018304663996866639456 - 9.0379068286817312753e-1863j 5.68e-132, 9.79e-364j
0.014057896901788855947 - 3.8534123800699317382e-1862j 2.87e-131, 4.94e-363j
0.00051694860958528336367 + 3.2092607492043596463e-1863j 6.81e-130, 1.17e-361j
0.024232200614055801685 - 1.9531153648252291029e-1861j 1.63e-135, 2.81e-367j
0.011357677472371628183 - 2.0737136153509796877e-1860j 6.43e-132, 1.11e-363j
0.015145320484031285894 + 7.1397789323051245374e-1863j 6.56e-132, 1.13e-363j
0.024232200614055801685 + 1.8898114172663053287e-1862j 2.23e-135, 3.83e-367j
0.0032962602749837408841 + 9.8145962880771782535e-1860j 2.21e-132, 3.81e-364j
0.021869794692814528308 - 2.4815137276542931585e-1861j 1.13e-135, 1.95e-367j
0.020418744012990465241 + 2.8754346814870147337e-1861j 2.87e-135, 4.94e-367j
0.019359204324247424098 + 1.2408883078368598165e-1862j 4.11e-135, 7.07e-367j
0.025177960697841506071 - 2.0212052857020010144e-1862j 3.66e-138, 6.31e-370j
0.016774664367445655334 + 3.7135793391022705047e-1863j 2.44e-134, 4.21e-366j
0.019359204324247424098 - 3.3143290486904229139e-1861j 4.86e-136, 8.37e-368j
0.02929234671461050196 + 1.317819220183188095e-1861j 1.23e-141, 2.12e-373j
0.016774664367445655334 - 4.8120195277596448241e-1861j 1.84e-135, 3.17e-367j
0.027695297675941631479 - 2.2312385258947021186e-1862j 1.03e-140, 1.77e-372j
0.028525731825552092478 + 2.3794110746630623857e-1862j 2.09e-141, 3.6e-373j
0.0022015550673638414115 - 2.4976444143206511541e-1860j 5.86e-136, 1.01e-367j
0.028525731825552092478 - 1.3900900123306233404e-1861j 2.89e-142, 4.98e-374j
0.025177960697841506071 + 1.7801190488702321013e-1861j 1.41e-140, 2.43e-372j
0.0076270726771964123728 - 3.4959966709350188409e-1862j 1.76e-138, 3.03e-370j
0.02929234671461050196 - 2.5420998787584782133e-1862j 1.37e-143, 2.36e-375j
0.026458648601187509448 + 2.1235777151118260044e-1862j 1.45e-141, 2.49e-373j
0.0076270726771964123728 - 2.6270865943303150382e-1860j 6.72e-138, 1.16e-369j
0.032125058483354362008 - 1.1559193632210858585e-1861j 2.68e-147, 4.62e-379j
0.0085675965947977731036 + 1.7600593571765565468e-1860j 4.85e-138, 8.35e-370j
0.023255804741329356602 - 1.7524138251822256565e-1862j 9.68e-142, 1.67e-373j
0.030406094802636208039 + 2.6891247192954493143e-1862j 5.56e-146, 9.57e-378j
0.021869794692814528308 + 1.6293043613781399123e-1862j 1.52e-141, 2.62e-373j
0.031499321528749931813 + 1.1853717130997446096e-1861j 9.7e-148, 1.67e-379j
0.027695297675941631479 + 1.4811251291134256325e-1861j 2.19e-145, 3.78e-377j
0.0095377965370229202187 - 5.8809066038891900759e-1862j 1.97e-141, 3.4e-373j
0.032638562811250639551 - 3.3718672136470315887e-1862j 6.14e-151, 1.06e-382j
0.0085675965947977731036 + 4.4524250542260734202e-1862j 2.18e-141, 3.76e-373j
0.030406094802636208039 - 1.2443430406410021262e-1861j 2.44e-148, 4.2e-380j
0.033598441087727618983 - 1.1153365436677659241e-1861j 3.89e-152, 6.69e-384j
0.023255804741329356602 + 2.1690932620902440618e-1861j 1.99e-145, 3.43e-377j
0.031499321528749931813 - 2.8580708630032957456e-1862j 6.01e-150, 1.04e-381j
0.032125058483354362008 + 3.0960575318059508884e-1862j 6.53e-151, 1.12e-382j
0.026458648601187509448 - 1.6159206834604049319e-1861j 1.4e-147, 2.42e-379j
0.032638562811250639551 + 1.1385580704943821901e-1861j 5.82e-152, 1e-383j
0.035904722280190747907 - 1.1848016548001704203e-1861j 7.43e-157, 1.28e-388j
0.033598441087727618983 + 3.6402628023807140697e-1862j 2.31e-154, 3.98e-386j
0.034935715036497732143 + 4.4289287451872390707e-1862j 1.55e-156, 2.67e-388j
0.039062284378767211245 - 1.3046844823427516088e-1861j 2.9e-160, 5e-392j
0.034935715036497732143 - 1.124030971842919912e-1861j 1.96e-156, 3.37e-388j
0.034588731648857103895 + 1.1032730943412373123e-1861j 1.88e-155, 3.25e-387j
0.040439002646744553049 + 2.584190772516136686e-1861j 6.84e-162, 1.18e-393j
0.035049852278642506433 - 4.9987518117535322153e-1862j 6.01e-159, 1.03e-390j
0.034588731648857103895 - 3.9611936877045742853e-1862j 3.7e-157, 6.38e-389j
0.030419482745967748692 - 3.7824531565164672374e-1861j 2.14e-162, 3.68e-394j
0.035049852278642506433 + 1.1598700233173954708e-1861j 5.17e-159, 8.9e-391j
0.039062284378767211245 + 1.8217625907285708538e-1861j 9.84e-163, 1.69e-394j
0.036895348172880893622 + 1.0730665095251871638e-1861j 7.6e-163, 1.31e-394j
0.035904722280190747907 + 5.5735463885330317937e-1862j 2.68e-161, 4.62e-393j
0.027541246810335031318 - 3.2280048414109258312e-1861j 1.2e-163, 2.08e-395j
0.036875882347887031253 - 1.3413911273378210213e-1861j 3.28e-163, 5.66e-395j
0.035999326770435202806 + 1.501052503639821621e-1861j 1.28e-163, 2.2e-395j
0.030419482745967748692 + 3.3520094152610162371e-1861j 2.88e-164, 4.96e-396j
0.036875882347887031253 + 7.506715097732648227e-1862j 2.16e-164, 3.72e-396j
0.035999326770435202806 - 9.1247324570363671047e-1862j 2.18e-164, 3.75e-396j
0.038490403557450440064 - 2.5156637481469695455e-1861j 1.21e-165, 2.09e-397j
0.036963294892482110467 + 1.2275590113439121593e-1861j 4.59e-165, 7.9e-397j
0.027541246810335031318 + 3.8506340743062818226e-1861j 1.34e-165, 2.3e-397j
0.038490403557450440064 + 1.9608495972950155113e-1861j 4.44e-166, 7.64e-398j
0.036963294892482110467 - 6.3020185641502740576e-1862j 2.97e-166, 5.1e-398j
0.040439002646744553049 - 2.4746660659450426318e-1861j 2.75e-166, 4.78e-398j
0.036895348172880893622 - 1.628404408037737573e-1861j 1.28e-166, 2.13e-398j

Download

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