Rule: Q[2, 3, 6, 12, 44]

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)
0.98785368285261173498 - 8.7712955848859824269e-798j 3.98e-229, 3.98e-229j
-0.051686314037462269989 + 1.3035292290339939116e-828j 2.6e-254, 2.6e-254j
-0.92582009977255146157 - 6.5003651690476638945e-797j 2.13e-230, 2.13e-230j
-0.99971857173370582681 - 2.7380703860439617709e-801j 8.72e-230, 8.72e-230j
0.92582009977255146157 + 9.2242369270185389621e-825j 2.12e-230, 2.12e-230j
0.96502643103930765951 + 7.532107557633398117e-822j 4.53e-229, 4.53e-229j
0.99971857173370582681 + 1.0798188447362774053e-823j 9.06e-230, 9.06e-230j
-0.94107813257443435158 + 4.6136332406740177785e-822j 6.87e-230, 6.87e-230j
-0.44696796404999669242 + 4.3299255177461422735e-853j 1.13e-243, 1.13e-243j
-0.99391986717259178359 + 4.7090487082623691957e-838j 3.36e-229, 3.36e-229j
0.90865970685622654079 + 1.9235728623614888441e-850j 6.69e-231, 6.69e-231j
0.99391986717259178359 - 2.1044281917100714766e-848j 3.15e-229, 3.15e-229j
-0.96502643103930765951 - 2.3947669573762806643e-845j 4.79e-229, 4.79e-229j
-0.86794828602803889807 + 1.2283130124089193666e-860j 4.11e-232, 4.11e-232j
0.65605621619432160035 + 2.9250753958212490436e-867j 5.74e-238, 5.74e-238j
0.88941079990763139894 + 1.5546314525705130383e-860j 1.71e-231, 1.71e-231j
0.94107813257443435158 + 1.9661081462488018901e-859j 6.75e-230, 6.75e-230j
-0.98785368285261173498 - 6.8318805498317682576e-856j 4.24e-229, 4.24e-229j
-0.81827149131976327701 + 4.0703487326535892311e-869j 1.45e-233, 1.45e-233j
-0.95442572227855990796 - 2.2144116196040495084e-863j 1.73e-229, 1.73e-229j
0.95442572227855990796 - 1.6711892572002721003e-873j 1.95e-229, 1.95e-229j
0.81827149131976327701 - 7.0222137410373753925e-879j 1.5e-233, 1.5e-233j
0.97228074954025767949 - 8.0700949323973432209e-874j 6.18e-229, 6.18e-229j
-0.84423396139053796111 + 3.7911187109858792905e-877j 8.98e-233, 8.98e-233j
-0.65605621619432160035 + 1.6147151718416887678e-882j 5.19e-238, 5.19e-238j
-0.99789629329501009199 - 4.6262332586445135978e-872j 2.32e-229, 2.32e-229j
0.75970689906559201289 + 6.6588666110365440822e-892j 3.58e-235, 3.58e-235j
0.57735026918962576451 - 5.8477078433117375527e-897j 3.96e-240, 3.96e-240j
0.99789629329501009199 - 5.7182875092243150883e-884j 2.36e-229, 2.36e-229j
-0.61759975043119467664 - 8.3266829911758568095e-896j 4.81e-239, 4.81e-239j
-0.10321869546611550579 + 1.3312473717709522948e-909j 6.32e-253, 6.32e-253j
0.79008322340119373077 - 1.9171475145033252129e-890j 2.38e-234, 2.38e-234j
0.72719603605765596578 - 3.1939903199365412915e-892j 4.48e-236, 4.48e-236j
0.25536489545589432869 + 5.2777311114380670812e-906j 6.9e-249, 6.9e-249j
-0.75970689906559201289 - 1.6280786598794038957e-890j 3.42e-235, 3.42e-235j
-0.72719603605765596578 - 2.4212038454040584966e-891j 4.43e-236, 4.43e-236j
0.10321869546611550579 + 8.9745979770304520723e-910j 5.34e-253, 5.34e-253j
0.61759975043119467664 + 5.1435050929161143494e-895j 4.89e-239, 4.89e-239j
0.6926188473346906128 + 1.4239135532739240034e-894j 5.26e-237, 5.26e-237j
0.98011593780931193107 - 1.7297319060819922151e-885j 5.57e-229, 5.57e-229j
-0.57735026918962576451 - 1.3097063452419699018e-895j 3.98e-240, 3.98e-240j
-0.88941079990763139894 + 3.875580843588103334e-884j 1.68e-231, 1.68e-231j
0.30476216915276288265 + 2.520417338133920265e-907j 1.68e-247, 1.68e-247j
0.86794828602803889807 + 5.2051165530717000564e-892j 3.94e-232, 3.94e-232j
-0.20520935349061247898 - 1.1241747121752454394e-909j 2.92e-250, 2.92e-250j
-0.6926188473346906128 + 3.5255268346941917651e-896j 5.34e-237, 5.34e-237j
-0.79008322340119373077 + 3.1493566441371855544e-894j 2.54e-234, 2.54e-234j
-0.97228074954025767949 + 8.2466566915817397518e-887j 6.55e-229, 6.55e-229j
0.49191505685339375848 + 7.2084656098535851841e-914j 1.96e-242, 1.96e-242j
-0.98011593780931193107 + 7.6338177220110680632e-905j 5.19e-229, 5.19e-229j
-0.90865970685622654079 + 9.7184560171589682996e-915j 6.38e-231, 6.38e-231j
-0.49191505685339375848 + 7.1243665718905481907e-927j 2.05e-242, 2.05e-242j
0.84423396139053796111 - 1.2223519502639864447e-933j 8.04e-233, 8.04e-233j
0.53541667280639575351 + 7.8296868151848495426e-942j 2.81e-241, 2.81e-241j
0.35325577397836760027 + 7.6397801484806154435e-947j 3.22e-246, 3.22e-246j
-0.30476216915276288265 + 3.6193135479968862321e-947j 1.41e-247, 1.41e-247j
-0.40070371325754278729 + 8.5513411652123143701e-944j 6.2e-245, 6.2e-245j
-0.25536489545589432869 + 2.7558469745436340869e-949j 6.84e-249, 6.84e-249j
6.6795867050466976402e-992 + 3.8117386471838858755e-992j 5.15e-990, 5.15e-990j
0.40070371325754278729 - 1.9663379175479012207e-945j 6.37e-245, 6.37e-245j
0.44696796404999669242 + 3.4041454748219715203e-944j 1.14e-243, 1.14e-243j
-0.53541667280639575351 - 2.0350330510797574825e-941j 2.89e-241, 2.89e-241j
-0.35325577397836760027 - 6.1102152958493200411e-947j 3.11e-246, 3.11e-246j
-0.15444378242844441647 + 1.4254987596145242795e-952j 1.25e-251, 1.25e-251j
0.20520935349061247898 + 5.6827502212706751464e-952j 2.95e-250, 2.95e-250j
0.15444378242844441647 + 3.3053372597998191855e-953j 1.35e-251, 1.35e-251j
0.051686314037462269989 - 6.0368247143110214435e-958j 2.81e-254, 2.81e-254j

Weights

Weight (ball center) Error (ball radius)
0.0070193694469278907469 + 3.3353611544545404434e-798j 2.7e-38, 2.21e-145j
0.051634974619434482991 + 3.4956314634427295705e-801j 1.29e-38, 1.05e-145j
0.016181044677629697177 + 2.7059041276929107665e-797j 3.63e-39, 2.97e-146j
0.00084548989216491509316 - 1.7777991952710397722e-798j 2.84e-39, 2.32e-146j
0.016181044677629697177 + 4.0412756175332769777e-799j 3.13e-39, 2.57e-146j
0.0086193905548522733996 - 6.8519945258246066138e-798j 2.7e-39, 2.21e-146j
0.00084548989216491509316 + 7.0061036478278760025e-799j 6.09e-40, 4.99e-147j
0.014342945706693320115 - 9.8938199326575021531e-797j 1.78e-40, 1.46e-147j
0.045627507781049383856 + 1.524268051952078833e-800j 1.31e-41, 1.07e-148j
0.0050546863979899148295 - 9.3548846214324772095e-798j 3.88e-41, 3.18e-148j
0.018174973069893625668 - 1.3046383984789812234e-799j 1.67e-40, 1.37e-147j
0.0050546863979899148295 + 6.33937512053785757e-798j 6.07e-40, 4.97e-147j
0.0086193905548522733996 - 8.8242196761519967644e-797j 1.8e-41, 1.48e-148j
0.022586846905666600563 + 5.7065099315612351872e-798j 2.74e-42, 2.24e-149j
0.037525627084590884787 - 1.1718790160093831175e-800j 2.33e-43, 1.91e-150j
0.020343594546722394246 + 1.5603120478651069293e-800j 2.32e-41, 1.9e-148j
0.014342945706693320115 - 1.0413322412335726789e-798j 1.38e-40, 1.13e-147j
0.0070193694469278907469 + 1.7343297934653970834e-797j 4.38e-42, 3.58e-149j
0.027080351535799417503 + 1.3728353089907122039e-798j 1.68e-44, 1.38e-151j
0.012234236497449919858 + 7.9794840895840696102e-797j 8.21e-42, 6.72e-149j
0.012234236497449919858 + 2.6988131870437983367e-798j 2.07e-41, 1.7e-148j
0.027080351535799417503 + 3.485399953615312391e-800j 3.18e-45, 2.61e-152j
0.0070226965762748603901 + 1.0732181185742210647e-797j 1.11e-41, 9.09e-149j
0.024840852390933881048 - 2.6984781009077049992e-798j 3.78e-45, 3.1e-152j
0.037525627084590884787 - 9.3679932664753639523e-800j 6.23e-48, 5.1e-155j
0.0028834050334671486472 + 5.1910212647291318852e-798j 4.85e-43, 3.97e-150j
0.031453799229262178307 + 2.3720139444108465593e-800j 1.37e-46, 1.12e-153j
0.041110315129527254413 - 7.6624175540736421282e-801j 6.99e-49, 5.73e-156j
0.0028834050334671486472 - 2.3241319198062680388e-798j 1.42e-42, 1.16e-149j
0.039370482784175382428 + 6.1199100040546084306e-800j 1.81e-49, 1.48e-156j
0.051404218431764549607 - 3.8524560178386521621e-801j 1.03e-50, 8.47e-158j
0.029289908600614164499 - 2.9461710940538796925e-800j 2.04e-46, 1.67e-153j
0.033556521554752581909 - 1.8747833258798595899e-800j 1.53e-47, 1.25e-154j
0.049800896624066626576 + 3.1685390110214902906e-801j 3.29e-52, 2.69e-159j
0.031453799229262178307 + 4.1528998972145227741e-799j 4.91e-50, 4.02e-157j
0.033556521554752581909 - 2.4354700418908344497e-799j 2.56e-50, 2.09e-157j
0.051404218431764549607 - 3.0040702006099103491e-801j 2.57e-53, 2.1e-160j
0.039370482784175382428 + 9.40388027636169829e-801j 3.05e-50, 2.5e-157j
0.035584342259087487407 + 1.4776279643143506508e-800j 3.34e-49, 2.74e-156j
0.0082244112350159826333 - 1.3886426968994140476e-797j 1.37e-45, 1.13e-152j
0.041110315129527254413 - 4.1302628610578083922e-800j 2.51e-53, 2.06e-160j
0.020343594546722394246 - 1.35720359562455911e-797j 5.01e-51, 4.1e-158j
0.048969407921771745292 - 3.3722915108390911159e-801j 1.18e-54, 9.65e-162j
0.022586846905666600563 + 2.6236391065521900024e-800j 2.29e-48, 1.88e-155j
0.05048547137363756016 - 5.0285317638783653938e-801j 4.77e-56, 3.91e-163j
0.035584342259087487407 + 1.4836654432706694782e-799j 2.4e-52, 1.96e-159j
0.029289908600614164499 - 7.3787788577218710757e-799j 9.01e-52, 7.38e-159j
0.0070226965762748603901 + 7.3319228738059101713e-797j 4.03e-51, 3.3e-158j
0.044245280961880075666 - 5.3707460039537887932e-801j 5.3e-57, 4.34e-164j
0.0082244112350159826333 - 3.7206215740452470001e-797j 2.6e-51, 2.13e-158j
0.018174973069893625668 + 4.2477756556197086888e-797j 3.93e-52, 3.22e-159j
0.044245280961880075666 - 2.0635634137660509603e-800j 1.6e-58, 1.31e-165j
0.024840852390933881048 - 3.6579846504803016709e-800j 2.36e-53, 1.94e-160j
0.042737516043285781651 + 6.3541102414673897316e-801j 1.84e-57, 1.51e-164j
0.04799412613299532685 + 3.6687052753501853321e-801j 1.27e-59, 1.04e-166j
0.048969407921771745292 - 7.246372991800584864e-801j 3.08e-61, 2.52e-168j
0.046878738958048869515 - 1.1579648877900120973e-800j 1.07e-60, 8.75e-168j
0.049800896624066626576 + 5.9607429504548433646e-801j 2.09e-61, 1.71e-168j
0.051711988505480899185 - 3.2473857594825869871e-801j 1.64e-62, 1.35e-169j
0.046878738958048869515 - 4.0785479839898854544e-801j 1.32e-61, 1.08e-168j
0.045627507781049383856 + 4.6318045550760089299e-801j 2.71e-61, 2.22e-168j
0.042737516043285781651 + 2.8758859022994926028e-800j 2.22e-61, 1.82e-168j
0.04799412613299532685 + 9.0397510627400400286e-801j 2.03e-62, 1.66e-169j
0.051020575789833372577 + 4.348295831048457789e-801j 2.37e-63, 1.94e-170j
0.05048547137363756016 - 3.0437609064180898451e-801j 1.21e-64, 9.92e-172j
0.051020575789833372577 + 2.9899634078236677062e-801j 5.84e-65, 4.82e-172j
0.051634974619434482991 + 3.0876847705295590832e-801j 5.22e-65, 4.19e-172j

Download

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