Rule: Q[10, 22, 32]

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)
0.99503552225733338949 + 5.5339397032077065816e-879j 9.32e-233, 9.32e-233j
-0.20029687400364056877 + 1.7319579511039671011e-910j 2.45e-250, 2.45e-250j
-0.93068335613097494988 - 8.8748864561353037039e-895j 1.88e-233, 1.88e-233j
0.3892557105883163005 - 2.9940030073751530532e-906j 1.9e-245, 1.9e-245j
0.96070517343788021741 - 2.0964058751947291266e-891j 4.95e-233, 4.95e-233j
0.93068335613097494988 + 2.8124668394798196154e-898j 1.63e-233, 1.63e-233j
-0.99503552225733338949 + 3.4270185089309014902e-901j 9.02e-233, 9.02e-233j
-0.91050643660687031693 - 1.4855857982725811664e-904j 6.82e-234, 6.82e-234j
-0.99897694834497812161 - 4.2380802790743614732e-902j 1.58e-233, 1.58e-233j
0.99124628433606588136 + 1.0847394286287064488e-904j 1.36e-232, 1.36e-232j
0.88811927075909637666 + 6.8167384154096855514e-923j 2.95e-234, 2.95e-234j
-0.3892557105883163005 + 7.9591246917528330446e-935j 1.9e-245, 1.9e-245j
-0.86506336668898451073 + 3.8290360724903719775e-923j 1.24e-234, 1.24e-234j
-0.83984317820585705589 - 3.4436939600520356948e-924j 3.5e-235, 3.5e-235j
0.98490035649425929769 - 1.9683961818821139491e-919j 9.57e-233, 9.57e-233j
0.86506336668898451073 - 1.2883661596330314902e-929j 1.09e-234, 1.09e-234j
0.83984317820585705589 - 1.3701196894177442717e-929j 3.38e-235, 3.38e-235j
-0.97390652851717172008 - 2.8209935639022282691e-926j 6.92e-233, 6.92e-233j
-0.74894036007656814279 + 2.3965149035349219725e-930j 4.9e-237, 4.9e-237j
-0.98490035649425929769 + 4.2071903435392282385e-925j 9.43e-233, 9.43e-233j
0.81102976272617322245 + 1.43896647469117447e-930j 8.98e-236, 8.98e-236j
0.78019809736326325075 - 4.3371149935305559133e-931j 2.38e-236, 2.38e-236j
0.14887433898163121088 - 1.0773532022862361861e-948j 8.48e-252, 8.48e-252j
-0.81102976272617322245 + 8.7084732564247809623e-932j 9.99e-236, 9.99e-236j
-0.78019809736326325075 + 6.8748869055709274001e-933j 2.28e-236, 2.28e-236j
0.91050643660687031693 - 4.2660719158973566171e-927j 7.44e-234, 7.44e-234j
0.74894036007656814279 + 4.8707894406789444518e-934j 4.98e-237, 4.98e-237j
0.94690803432386905048 + 3.6085591335197431183e-929j 3.58e-233, 3.58e-233j
-0.94690803432386905048 + 3.3477781540176298139e-936j 3.55e-233, 3.55e-233j
-0.6412315050581950258 - 2.2538335953447178611e-954j 2.32e-239, 2.32e-239j
0.049789749661096719945 - 1.5310743437813694624e-969j 3.16e-254, 3.16e-254j
0.6412315050581950258 + 3.7360403884695705759e-952j 2.15e-239, 2.15e-239j
0.67940956829902440623 - 3.8782450895072390398e-951j 1.53e-238, 1.53e-238j
0.094446813277325511838 + 3.5140451161612509097e-967j 3.12e-253, 3.12e-253j
-0.67940956829902440623 + 5.4013711045506972771e-953j 1.56e-238, 1.56e-238j
-0.71584751120608567206 + 8.4487624735466512107e-952j 1.08e-237, 1.08e-237j
-0.14887433898163121088 - 4.9878122269869382979e-966j 7.69e-252, 7.69e-252j
0.56360426581820408261 + 3.8304601521057540524e-954j 3.58e-241, 3.58e-241j
0.022645032825774218315 + 1.3511886226377198471e-969j 4.59e-255, 4.59e-255j
0.97390652851717172008 - 1.3331883292078933215e-945j 6.56e-233, 6.56e-233j
-0.60312663471123618802 + 1.6649958475257785471e-967j 3.26e-240, 3.26e-240j
-0.96070517343788021741 - 2.8195815492778395577e-960j 5.14e-233, 5.14e-233j
0.71584751120608567206 - 3.9743053362271032928e-977j 1.04e-237, 1.04e-237j
0.52084921768775535553 + 9.9832346807842452157e-984j 3.49e-242, 3.49e-242j
0.99897694834497812161 - 3.0692733895950627408e-974j 1.48e-233, 1.48e-233j
-0.56360426581820408261 + 1.454206413534858566e-994j 3.5e-241, 3.5e-241j
-0.52084921768775535553 + 4.1661904639414923686e-997j 3.59e-242, 3.59e-242j
0.20029687400364056877 + 1.4978198546487069399e-1004j 2.32e-250, 2.32e-250j
0.47666535546708534709 - 1.392646723992220227e-997j 2.89e-243, 2.89e-243j
0.60312663471123618802 + 1.6500803747103026322e-994j 3.15e-240, 3.15e-240j
-0.29278090980112349149 - 4.0183656933251964409e-1002j 6.25e-248, 6.25e-248j
-0.4333953941292471908 - 1.3175870844403338815e-998j 2.57e-244, 2.57e-244j
-0.88811927075909637666 - 2.6795065341122098131e-991j 3.33e-234, 3.33e-234j
0.29278090980112349149 + 4.3594447055598441791e-1007j 5.75e-248, 5.75e-248j
0.34163474874369267131 - 1.0594598129037040945e-1005j 1.2e-246, 1.2e-246j
-0.99124628433606588136 + 4.0235193787889223068e-1008j 1.27e-232, 1.27e-232j
-0.47666535546708534709 + 8.7250608279446088147e-1023j 3.11e-243, 3.11e-243j
-0.24647926515375348297 + 4.3901568308819832615e-1028j 4.14e-249, 4.14e-249j
-0.094446813277325511838 + 7.2177060031279872688e-1033j 3.79e-253, 3.79e-253j
0.4333953941292471908 + 3.3004736827610325452e-1024j 2.57e-244, 2.57e-244j
0.24647926515375348297 - 1.7869419193797155964e-1028j 3.99e-249, 3.99e-249j
-0.049789749661096719945 - 2.5993191185056662201e-1034j 3.63e-254, 3.63e-254j
-0.34163474874369267131 + 1.4508605847800741168e-1025j 1.15e-246, 1.15e-246j
-0.022645032825774218315 + 1.2667009822104573879e-1034j 4.59e-255, 4.59e-255j

Weights

Weight (ball center) Error (ball radius)
0.0047035142957517297283 - 8.4219905827570416761e-879j 1.88e-47, 3.17e-158j
0.04854420475426070735 + 1.1331616793100679084e-879j 6.88e-48, 1.16e-158j
0.018334045529723370098 + 5.6699392511683530411e-881j 2.12e-48, 3.58e-159j
0.045849346428670544086 - 1.0864191193454806816e-879j 2.34e-48, 3.96e-159j
0.013595914534248134587 - 2.2788879660025934019e-879j 3.43e-48, 5.8e-159j
0.018334045529723370098 - 1.6967119698575315559e-879j 1.99e-48, 3.36e-159j
0.0047035142957517297283 + 1.307941471617355116e-881j 3.91e-49, 6.6e-160j
0.021664950833803353221 - 6.1822577167921521897e-881j 5.21e-49, 8.79e-160j
0.0025962879692125745388 - 2.0371216104536957537e-882j 2.96e-49, 5e-160j
0.0035697699291224299015 + 1.3048000068236556786e-878j 5.19e-49, 8.76e-160j
0.022780455922070009467 - 1.3332822070544209434e-879j 1.7e-49, 2.86e-160j
0.045849346428670544086 + 4.754279691259991121e-880j 2.24e-50, 3.78e-161j
0.02365794774561185712 - 9.0454862003373824245e-881j 2.14e-50, 3.61e-161j
0.027083589462498667892 + 9.7865935758398073677e-881j 1.14e-50, 1.92e-161j
0.0091915908189994485509 - 5.0768892473554284489e-879j 5.47e-50, 9.23e-161j
0.02365794774561185712 + 1.2945464170882910401e-879j 2.77e-51, 4.67e-162j
0.027083589462498667892 - 1.1570939412088768178e-879j 4.26e-52, 7.19e-163j
0.012442116334881039228 - 2.8094887155593748802e-881j 3.5e-52, 5.91e-163j
0.031707657825529421889 - 1.4612779533386449459e-880j 6.47e-54, 1.09e-164j
0.0091915908189994485509 + 2.5988272971311087715e-881j 4.97e-52, 8.39e-163j
0.03021485347113782416 + 1.0434584208961153954e-879j 4.27e-53, 7.21e-164j
0.03111075739685260358 - 1.0350143067569162891e-879j 7.3e-54, 1.23e-164j
0.053783511102169155526 + 1.9842735577160744736e-879j 9e-57, 1.52e-167j
0.03021485347113782416 - 1.0630975572842727586e-880j 5.64e-54, 9.52e-165j
0.03111075739685260358 + 1.2525664562375361598e-880j 2.32e-54, 3.92e-165j
0.021664950833803353221 + 1.3936683910873735477e-879j 1.06e-53, 1.79e-164j
0.031707657825529421889 + 1.0355479910396621077e-879j 9.9e-56, 1.67e-166j
0.014411656506440257347 + 2.106243347838559055e-879j 3.88e-54, 6.55e-165j
0.014411656506440257347 - 5.21993551072060232e-881j 2.67e-55, 4.5e-166j
0.038235144909014943194 + 2.0347285360885405299e-880j 4.66e-58, 7.86e-169j
0.028595602925742214201 + 8.4199602441094695489e-879j 1.32e-59, 2.22e-170j
0.038235144909014943194 - 9.4101792271783159076e-880j 3e-58, 5.06e-169j
0.037736716775517547453 + 9.1871873675533646819e-880j 1.16e-57, 1.96e-168j
0.053691096912897019536 - 3.5279758313341350831e-879j 9.07e-60, 1.53e-170j
0.037736716775517547453 - 1.7317467102575393684e-880j 3.83e-59, 6.47e-170j
0.034804834978364776921 + 1.5859989389299547751e-880j 1.2e-58, 2.03e-169j
0.053783511102169155526 - 1.4677863338997640603e-879j 9.98e-62, 1.68e-172j
0.041154610514931151451 - 9.4529678958253792233e-880j 3.3e-61, 5.57e-172j
0.039417605970376560165 - 1.0005018064914391154e-878j 6.08e-61, 1.03e-171j
0.012442116334881039228 + 2.6180709508810800091e-879j 2.99e-58, 5.05e-169j
0.038288764778484107687 - 2.3825130817442226104e-880j 7.28e-62, 1.23e-172j
0.013595914534248134587 + 4.0002756482760379494e-881j 3.64e-60, 6.15e-171j
0.034804834978364776921 - 9.7191088739410360527e-880j 8.69e-60, 1.47e-170j
0.043982510670182028936 + 9.2782169978298812884e-880j 1.85e-62, 3.11e-173j
0.0025962879692125745388 - 1.030603087576054374e-879j 1.54e-59, 2.61e-170j
0.041154610514931151451 + 2.6165800767926620476e-880j 3.16e-63, 5.34e-174j
0.043982510670182028936 - 2.902333742969833289e-880j 5.76e-64, 9.73e-175j
0.04854420475426070735 - 1.7043399971262332125e-879j 1.15e-64, 1.94e-175j
0.043890179206041486014 - 9.923113283339267418e-880j 5.73e-64, 9.67e-175j
0.038288764778484107687 + 9.7156312773800446627e-880j 1.66e-62, 2.81e-173j
0.047994449381714301429 + 7.1133403648718080847e-880j 1.01e-66, 1.71e-177j
0.043009890260464761225 - 4.2186926217548131467e-880j 3.25e-66, 5.49e-177j
0.022780455922070009467 + 7.5697195098466850663e-881j 5.42e-65, 9.14e-176j
0.047994449381714301429 - 1.3044665632976191799e-879j 1.31e-66, 2.21e-177j
0.048934039930641145715 + 1.1184389671838874937e-879j 2.01e-66, 3.39e-177j
0.0035697699291224299015 - 2.4891723063223759778e-881j 1.81e-65, 3.05e-176j
0.043890179206041486014 + 3.4951707684762225578e-880j 1.45e-66, 2.45e-177j
0.045022381924644827801 - 9.4086131664209770115e-880j 1.14e-67, 1.93e-178j
0.053691096912897019536 + 2.916298039559000324e-879j 2.37e-68, 3.99e-179j
0.043009890260464761225 + 1.0729487915564587172e-879j 8.32e-68, 1.4e-178j
0.045022381924644827801 + 1.5604615236722129386e-879j 4.12e-68, 6.96e-179j
0.028595602925742214201 - 7.6174763762741568429e-879j 6.74e-69, 1.14e-179j
0.048934039930641145715 - 5.4672337833807938362e-880j 6.49e-70, 1.11e-180j
0.039417605970376560165 + 9.5597625053563224429e-879j 8.13e-69, 1.37e-179j

Download

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