Rule: Q[10, 22, 33]

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)
0.99124628433606588136 - 1.0539716945204439551e-843j 9e-231, 9e-231j
-0.97390652851717172008 + 1.0895402892837749188e-863j 2.62e-231, 2.62e-231j
-0.92986205036554551416 + 1.5710258149083843406e-862j 2.2e-232, 2.2e-232j
-0.99974331108681322325 - 2.1404685156114111622e-859j 1.5e-230, 1.5e-230j
0.78095546704874354397 - 1.9490232814334632827e-869j 9.23e-236, 9.23e-236j
0.92986205036554551416 + 1.4560669476672243564e-863j 2.08e-232, 2.08e-232j
0.99897694834497812161 + 1.4406332113533990115e-867j 2.73e-230, 2.73e-230j
-0.91050643660687031693 - 9.9121835184406796374e-903j 7.92e-233, 7.92e-233j
-0.99629483063339791056 - 4.8409560872274633624e-899j 1.8e-230, 1.8e-230j
0.99974331108681322325 + 1.4723985615138036896e-896j 1.48e-230, 1.48e-230j
0.86506336668898451073 - 3.3918521407540719271e-918j 7.58e-234, 7.58e-234j
0.96160203973280612137 - 1.4026063072083476923e-914j 1.23e-231, 1.23e-231j
-0.86506336668898451073 + 4.0404870775768524478e-922j 7.58e-234, 7.58e-234j
-0.88888897592962552352 + 7.6372669921788612547e-922j 2.61e-233, 2.61e-233j
0.99629483063339791056 - 5.9565531146595985723e-916j 1.68e-230, 1.68e-230j
0.83908884889973318452 - 2.8704103435805810496e-928j 1.97e-234, 1.97e-234j
0.91050643660687031693 + 1.6200901460864434131e-925j 8.82e-233, 8.82e-233j
-0.99124628433606588136 - 7.6862832955107909227e-922j 9.09e-231, 9.09e-231j
-0.78095546704874354397 - 1.2808122412699190654e-930j 9.83e-236, 9.83e-236j
-0.96160203973280612137 - 9.3086798250429304224e-926j 1.23e-231, 1.23e-231j
0.88888897592962552352 - 8.134350329613960836e-927j 2.62e-233, 2.62e-233j
0.81102976272617322245 - 2.5852359601084602508e-928j 4.7e-235, 4.7e-235j
-0.94690803432386905048 - 1.3506171594217161464e-925j 5.75e-232, 5.75e-232j
-0.83908884889973318452 + 1.6126014870797152707e-928j 1.9e-234, 1.9e-234j
-0.81102976272617322245 - 3.1357043365856772954e-929j 4.53e-235, 4.53e-235j
0.97390652851717172008 - 1.7743131560769901105e-924j 2.7e-231, 2.7e-231j
0.71506373924643323295 + 3.2873176221778499957e-939j 2.89e-237, 2.89e-237j
0.74894036007656814279 - 1.1084054679225399422e-939j 1.68e-236, 1.68e-236j
-0.99897694834497812161 - 9.0167961783228122801e-929j 2.56e-230, 2.56e-230j
-0.6420662865421718939 + 1.0794294587896442318e-941j 5.45e-239, 5.45e-239j
-0.98379164853935874028 - 1.2665783650920974872e-932j 4.83e-231, 4.83e-231j
0.67940956829902440623 - 4.071189114779002173e-941j 4.25e-238, 4.25e-238j
0.6420662865421718939 + 6.2682654415098573445e-942j 5.03e-239, 5.03e-239j
-0.19792283445893261195 + 1.5318518094341209885e-953j 2.33e-250, 2.33e-250j
-0.71506373924643323295 - 3.0751330362484307117e-941j 2.87e-237, 2.87e-237j
-0.67940956829902440623 + 4.1305413353187404616e-942j 3.91e-238, 3.91e-238j
0.94690803432386905048 + 6.9183024960933269877e-938j 5.6e-232, 5.6e-232j
0.60312663471123618802 + 2.6616124189665471845e-952j 5.91e-240, 5.91e-240j
0.98379164853935874028 - 1.7371191925644861209e-956j 5.19e-231, 5.19e-231j
-0.47771610970551796541 + 3.26088421607235601e-979j 4.68e-243, 4.68e-243j
-0.52084921768775535553 - 7.5227509991001927128e-978j 5.39e-242, 5.39e-242j
-0.74894036007656814279 + 1.1205070838207102108e-979j 1.73e-236, 1.73e-236j
0.34163474874369267131 - 9.8744995842442689463e-991j 1.64e-246, 1.64e-246j
0.56268741793455933558 + 4.7804104046329068789e-985j 6.74e-241, 6.74e-241j
-0.049789749661096719945 + 2.045038302778905131e-998j 2.06e-254, 2.06e-254j
-0.56268741793455933558 + 2.2711070984168341146e-983j 6.22e-241, 6.22e-241j
-0.60312663471123618802 + 4.2708293349849554454e-989j 6.08e-240, 6.08e-240j
0.099455692377556159028 - 2.2180137198156894426e-1001j 4.66e-253, 4.66e-253j
0.47771610970551796541 - 1.1575739508032355346e-988j 4.58e-243, 4.58e-243j
0.29442295370714073822 - 4.8500735328089008757e-995j 9.07e-248, 9.07e-248j
-0.14887433898163121088 - 7.0571581457233713113e-1000j 9.77e-252, 9.77e-252j
-0.4333953941292471908 - 2.9277187056668084629e-992j 3.61e-244, 3.61e-244j
-0.099455692377556159028 + 7.3152769085861174939e-1001j 3.82e-253, 3.82e-253j
0.52084921768775535553 + 1.3097181342079861276e-989j 5.55e-242, 5.55e-242j
0.4333953941292471908 + 8.3619279257296904619e-992j 3.87e-244, 3.87e-244j
0.049789749661096719945 + 1.8132861460397561017e-1003j 2e-254, 2e-254j
-0.34163474874369267131 - 6.7767646964473278895e-995j 1.6e-246, 1.6e-246j
-0.29442295370714073822 + 2.8176659104629582534e-996j 8.58e-248, 8.58e-248j
0.14887433898163121088 + 5.9752961895413928024e-1000j 1.07e-251, 1.07e-251j
0.3879973116919424432 - 9.1394708419162834172e-993j 2.9e-245, 2.9e-245j
0.19792283445893261195 - 2.8208260027957084151e-998j 2.46e-250, 2.46e-250j
-0.24647926515375348297 - 2.2822435234379736503e-997j 4.16e-249, 4.16e-249j
-0.3879973116919424432 + 1.295616489548556091e-993j 2.72e-245, 2.72e-245j
-1.5401784948817625993e-1039 - 7.5874290457833230278e-1040j 1.12e-1037, 1.12e-1037j
0.24647926515375348297 + 5.1189336487984573572e-997j 4.37e-249, 4.37e-249j

Weights

Weight (ball center) Error (ball radius)
0.0062439994744623640246 - 5.0923861682774527079e-844j 5.52e-31, 1.9e-139j
0.011098753230635199754 + 2.0804101410917439014e-846j 2.48e-31, 8.55e-140j
0.018208276359060739368 - 1.3448388419322934456e-846j 1.75e-31, 6.03e-140j
0.00047155711376732186607 - 3.7096338806554626362e-846j 7.05e-32, 2.43e-140j
0.031057516881049420039 - 7.3397265477593289717e-846j 1.97e-32, 6.78e-141j
0.018208276359060739368 - 4.208867555971048739e-845j 2.25e-32, 7.76e-141j
0.001498303773149939448 - 1.651574027395317911e-843j 6.71e-33, 2.31e-141j
0.020494996232822405251 + 1.2135138481705151019e-846j 9.47e-34, 3.26e-142j
0.0038626982234116031569 - 4.5970163307193776101e-846j 1.93e-33, 6.64e-142j
0.00047155711376732186607 + 8.6922669256787009336e-844j 5.06e-33, 1.74e-141j
0.024910370332751872062 + 1.5157507832009386671e-845j 2.53e-35, 8.71e-144j
0.013505067131615795673 - 1.1536357030612050127e-844j 7.57e-35, 2.61e-143j
0.024910370332751872062 + 1.0303337923418582485e-846j 2.36e-36, 8.11e-145j
0.022730966381242796023 - 1.1112694884421543817e-846j 8.57e-36, 2.95e-144j
0.0038626982234116031569 + 1.8097801674749805652e-843j 1.24e-33, 4.26e-142j
0.027027941545217458823 - 1.1614355844982449324e-845j 1.16e-36, 4.01e-145j
0.020494996232822405251 + 2.8583200582699478615e-845j 6.57e-36, 2.26e-144j
0.0062439994744623640246 + 3.3195578186160949492e-846j 7.05e-37, 2.43e-145j
0.031057516881049420039 - 8.7093757422803796647e-847j 5.65e-40, 1.95e-148j
0.013505067131615795673 - 1.7512194133615587551e-846j 2.27e-37, 7.83e-146j
0.022730966381242796023 - 2.0412191189916532445e-845j 3.96e-37, 1.36e-145j
0.029078672100484820457 + 9.1327760309470542474e-846j 2.46e-38, 8.49e-147j
0.015876653170817958373 + 1.5174102438098687034e-846j 1.73e-37, 5.97e-146j
0.027027941545217458823 - 9.6551203521581734041e-847j 8.89e-40, 3.06e-148j
0.029078672100484820457 + 9.1322144108961883681e-847j 1.73e-40, 5.94e-149j
0.011098753230635199754 + 2.3577747480157819501e-844j 3.32e-39, 1.14e-147j
0.034779768157791035662 - 5.0019920853011665001e-846j 2.35e-43, 8.09e-152j
0.03295947650591894446 + 6.0100421853390519699e-846j 2.16e-42, 7.45e-151j
0.001498303773149939448 + 6.415242110524521206e-846j 1.02e-38, 3.53e-147j
0.038157271490143497214 - 7.7208556512489478598e-847j 3.65e-47, 1.26e-155j
0.0086692946606831520897 - 2.5652791964049255974e-846j 2.49e-39, 8.59e-148j
0.036513831218564996217 + 4.2231662810610066257e-846j 1.44e-45, 4.95e-154j
0.038157271490143497214 - 3.6114813771677349667e-846j 1.12e-46, 3.87e-155j
0.048822688682706976835 - 8.3117863296983525805e-847j 2e-51, 6.89e-160j
0.034779768157791035662 - 8.0962010745046895637e-847j 6.61e-47, 2.28e-155j
0.036513831218564996217 + 7.8827623432273657247e-847j 1.89e-47, 6.52e-156j
0.015876653170817958373 + 6.6330430641937806039e-845j 1.18e-43, 4.07e-152j
0.039705892992720939618 + 3.124127603351152459e-846j 3.31e-49, 1.14e-157j
0.0086692946606831520897 - 6.7964738445758662831e-844j 3.66e-43, 1.26e-151j
0.043745050004288835316 - 7.5009865390877885762e-847j 1.87e-52, 6.45e-161j
0.042503277857131756479 + 7.497439500051455885e-847j 4.89e-52, 1.68e-160j
0.03295947650591894446 + 8.3684634130075500313e-847j 2.78e-48, 9.59e-157j
0.046806570288010406043 + 1.5864139888694245741e-846j 1.62e-55, 5.58e-164j
0.041155772282038561646 - 2.7309008537533948811e-846j 3.31e-52, 1.14e-160j
0.049748464805343635855 + 9.3193862113822853477e-847j 1.34e-56, 4.61e-165j
0.041155772282038561646 - 7.531542513231615575e-847j 2.7e-52, 9.31e-161j
0.039705892992720939618 + 7.6050922360149207033e-847j 1.01e-51, 3.49e-160j
0.049562833800968927469 - 1.0919425520487660952e-846j 7.41e-58, 2.55e-166j
0.043745050004288835316 - 2.1456708268524469098e-846j 8.84e-56, 3.04e-164j
0.047597458740456924771 - 1.454606102477095e-846j 3.61e-57, 1.24e-165j
0.049253978439829144921 + 8.5941447263154467176e-847j 1.08e-57, 3.71e-166j
0.044878002697157487355 + 7.5412300239986427481e-847j 1.88e-56, 6.46e-165j
0.049562833800968927469 - 8.9280492349555408058e-847j 6.98e-58, 2.4e-166j
0.042503277857131756479 + 2.4100585119505975157e-846j 2.68e-56, 9.24e-165j
0.044878002697157487355 + 1.9258821286633342291e-846j 1.9e-57, 6.53e-166j
0.049748464805343635855 + 1.0305113941489329599e-846j 2.1e-59, 7.24e-168j
0.046806570288010406043 + 7.7317690162751495039e-847j 2.43e-59, 8.35e-168j
0.047597458740456924771 - 7.8838587646691867523e-847j 1.48e-59, 5.09e-168j
0.049253978439829144921 + 1.1631870809902777596e-846j 1.28e-60, 4.39e-169j
0.045899343065049785316 - 1.7417433843594369689e-846j 7.45e-60, 2.56e-168j
0.048822688682706976835 - 1.2459129535160617229e-846j 5.08e-61, 1.76e-169j
0.04827005499508152559 + 8.0762593224212458841e-847j 5.61e-61, 1.95e-169j
0.045899343065049785316 - 7.6179792333303848625e-847j 7.45e-61, 2.59e-169j
0.049810394731247545648 - 9.7754276584650406478e-847j 2e-61, 7.1e-170j
0.04827005499508152559 + 1.3421905441840105001e-846j 1.76e-61, 5.82e-170j

Download

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