Rule: Q[2, 3, 6, 22, 34]

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)
0.99367275813342635148 + 2.1221967584625747134e-856j 3.19e-229, 3.19e-229j
-0.96296251862632594359 + 2.842956110753122668e-854j 3.24e-229, 3.24e-229j
-0.95247411416333978885 + 9.101860474730824647e-867j 1.71e-229, 1.71e-229j
-0.9995948303654256396 + 7.9106728985815554353e-882j 7.41e-230, 7.41e-230j
0.96296251862632594359 + 2.6092070202666116862e-893j 3.16e-229, 3.16e-229j
0.92582009977255146157 + 1.4685704085814592043e-895j 2.6e-230, 2.6e-230j
0.99761564752831530681 + 1.665762239054093655e-893j 2.13e-229, 2.13e-229j
-0.90896196749502834257 - 1.9179477863293830082e-894j 7.76e-231, 7.76e-231j
-0.97220928203468039914 + 2.7832289483885631307e-895j 4.41e-229, 4.41e-229j
-0.99761564752831530681 - 7.4592095497381301795e-906j 2.16e-229, 2.16e-229j
0.88972209068447914916 + 2.849105811708584711e-920j 1.85e-231, 1.85e-231j
0.97220928203468039914 - 4.3841785704469831424e-917j 4.48e-229, 4.48e-229j
-0.940258249276585613 + 2.0726523570261369184e-917j 8.13e-230, 8.13e-230j
-0.88972209068447914916 + 7.7838653680267403797e-927j 1.91e-231, 1.91e-231j
0.61759188398688228631 - 1.6683022185086892904e-939j 4.87e-239, 4.87e-239j
0.90896196749502834257 + 1.6660821329997628725e-931j 7.33e-231, 7.33e-231j
0.95247411416333978885 - 1.6598346859578394208e-929j 1.96e-229, 1.96e-229j
-0.98054341784326322582 + 6.4302865143413398432e-927j 4.63e-229, 4.63e-229j
-0.79008322340119373077 - 1.300612340180584995e-951j 2.4e-234, 2.4e-234j
0.868172269613032014 + 1.562273041973507624e-947j 4.5e-232, 4.5e-232j
0.98785368285261173498 + 9.5778693404736578608e-944j 4.2e-229, 4.2e-229j
0.79008322340119373077 + 1.8239435214379226204e-951j 2.6e-234, 2.6e-234j
0.81832146626913634583 - 3.761677333997583386e-950j 1.5e-233, 1.5e-233j
-0.81832146626913634583 - 6.9167608121675659074e-951j 1.48e-233, 1.48e-233j
-0.75968193231455963371 - 1.250961994765887379e-951j 3.63e-235, 3.63e-235j
-0.99367275813342635148 - 3.6379210298258251357e-944j 3.33e-229, 3.33e-229j
0.75968193231455963371 - 5.272653830566380063e-961j 3.61e-235, 3.61e-235j
0.53542164912311694041 + 2.8106062927978600569e-968j 2.88e-241, 2.88e-241j
0.9995948303654256396 - 6.5192864799233259694e-953j 7.94e-230, 7.94e-230j
-0.65603855443711485605 - 1.0521222324042584609e-966j 5.38e-238, 5.38e-238j
-0.10321575447435615671 + 1.5918373411293286944e-983j 5.72e-253, 5.72e-253j
0.84436108167932387319 - 1.3678887527725033151e-958j 8.61e-233, 8.61e-233j
0.72716455684343167249 + 2.5432499022736621422e-963j 4.43e-236, 4.43e-236j
0.65603855443711485605 + 6.5308272128122510357e-965j 5.4e-238, 5.4e-238j
-0.72716455684343167249 + 3.7804938467358344183e-964j 4.67e-236, 4.67e-236j
-0.69259188218200868094 + 6.1248119192979590895e-965j 5.22e-237, 5.22e-237j
-9.744083140687473902e-1019 + 1.2901806292757191051e-1018j 1.08e-1016, 1.08e-1016j
0.69259188218200868094 - 1.2444313968232488628e-963j 5.35e-237, 5.35e-237j
0.40070877258142725562 + 7.083398916825722493e-973j 6.34e-245, 6.34e-245j
-0.051684660541093552855 - 7.7681995797386093451e-983j 2.85e-254, 2.85e-254j
-0.57735026918962576451 + 2.4435539478202561799e-968j 3.98e-240, 3.98e-240j
-0.92582009977255146157 + 4.7289247101124104268e-957j 2.73e-230, 2.73e-230j
0.98054341784326322582 + 2.8647387987071959803e-957j 4.5e-229, 4.5e-229j
0.44697480101938846011 + 5.6928285248589259754e-974j 1.2e-243, 1.2e-243j
-0.25536284723398172029 - 1.5525085441161684344e-978j 7.58e-249, 7.58e-249j
-0.53542164912311694041 + 4.6545833935195620395e-971j 2.8e-241, 2.8e-241j
-0.30476216915276288265 + 4.9396167558283196684e-977j 1.42e-247, 1.42e-247j
-0.98785368285261173498 + 7.5416670435086863409e-962j 4.07e-229, 4.07e-229j
0.49192212771516655197 + 2.0290027918149393411e-978j 1.98e-242, 1.98e-242j
0.940258249276585613 + 1.7506554636655103625e-971j 7.45e-230, 7.45e-230j
-0.868172269613032014 - 5.7217307580487513105e-971j 4.32e-232, 4.32e-232j
-0.49192212771516655197 + 7.1045562467993330838e-983j 2.08e-242, 2.08e-242j
0.20520608093988050927 + 1.2968307037284997988e-991j 3.06e-250, 3.06e-250j
0.57735026918962576451 + 1.3856772752911840079e-981j 4.08e-240, 4.08e-240j
0.25536284723398172029 + 1.0018151757143979854e-990j 6.58e-249, 6.58e-249j
-0.15444023231134406481 - 4.8095360110861676738e-995j 1.25e-251, 1.25e-251j
-0.44697480101938846011 - 1.6829580567209435615e-984j 1.11e-243, 1.11e-243j
-0.20520608093988050927 - 3.9332654644575868137e-993j 2.95e-250, 2.95e-250j
0.10321575447435615671 + 3.6045152302540378173e-995j 6.29e-253, 6.29e-253j
0.35325831973351427588 - 1.2419676138553567672e-987j 3.26e-246, 3.26e-246j
0.051684660541093552855 + 1.6119248128997128047e-996j 2.85e-254, 2.85e-254j
-0.35325831973351427588 - 5.7937681771120135986e-988j 3.14e-246, 3.14e-246j
-0.40070877258142725562 + 1.9696275967630720378e-986j 6.52e-245, 6.52e-245j
-0.84436108167932387319 - 2.0995807957642319891e-986j 8.42e-233, 8.42e-233j
0.30476216915276288265 + 4.6596843013872386489e-1003j 1.59e-247, 1.59e-247j
0.15444023231134406481 - 4.6053026730807622282e-1007j 1.23e-251, 1.23e-251j
-0.61759188398688228631 - 5.6816791122401577064e-998j 4.9e-239, 4.9e-239j

Weights

Weight (ball center) Error (ball radius)
0.0049252454153189753459 - 3.5326639477443801331e-857j 5.56e-39, 1.2e-145j
0.0097961155923882118546 - 7.1269152462203534235e-856j 2.68e-39, 5.77e-146j
0.011260528728541821081 - 2.4787911012924592305e-854j 2.31e-39, 4.97e-146j
0.0010811464357337118541 - 3.2401892769294655549e-856j 2e-40, 4.31e-147j
0.0097961155923882118546 + 4.0607603043655381666e-858j 6.69e-41, 1.44e-147j
0.015643726907242433182 - 4.1155153998650780876e-857j 3.18e-41, 6.85e-148j
0.0029421748730107553494 - 1.6434399140933822793e-856j 8.08e-41, 1.74e-147j
0.01806226116616042517 + 1.6301196128972910617e-855j 2e-41, 4.3e-148j
0.0087605827865204904914 + 2.6041573144456247038e-854j 9.79e-41, 2.11e-147j
0.0029421748730107553494 + 1.0682710251713465261e-855j 3.98e-41, 8.57e-148j
0.020404961846011410686 - 2.198819748956640333e-857j 3.11e-43, 6.69e-150j
0.0087605827865204904914 + 4.9435205838004320472e-857j 1.88e-42, 4.04e-149j
0.0132625721642480097 + 8.8487227435008888038e-855j 1.86e-41, 4e-148j
0.020404961846011410686 - 7.6801387530391379531e-856j 4.86e-43, 1.05e-149j
0.039361386592938934917 + 1.1984714301623776201e-858j 4.34e-46, 9.33e-153j
0.01806226116616042517 + 3.093396854875544343e-857j 3.12e-43, 6.72e-150j
0.011260528728541821081 - 3.7934688711683940046e-857j 7.29e-43, 1.57e-149j
0.0078868353061241253644 - 9.8148335975154790833e-855j 1.37e-42, 2.94e-149j
0.029326513939272269829 - 6.1934228046332690886e-857j 9.68e-47, 2.08e-153j
0.022686822118922044262 + 1.5353966124045632964e-857j 7.8e-45, 1.68e-151j
0.006646487931069068069 + 2.3777025150613403638e-856j 1.46e-43, 3.15e-150j
0.029326513939272269829 - 5.3006363827052245558e-858j 3.2e-47, 6.88e-154j
0.02714413577874068379 + 7.4938778442841371141e-858j 1.11e-46, 2.39e-153j
0.02714413577874068379 + 1.0939728157566906542e-856j 9.84e-49, 2.12e-155j
0.031468279421243146442 + 3.6271788700880206764e-857j 1.02e-49, 2.19e-156j
0.0049252454153189753459 - 2.1966492171623936557e-855j 6.6e-46, 1.42e-152j
0.031468279421243146442 + 3.798716928603366774e-858j 1.5e-48, 3.24e-155j
0.042734039808429155786 + 7.6524849183408773119e-859j 5.04e-52, 1.08e-158j
0.0010811464357337118541 + 3.7099812714681141572e-857j 2.75e-46, 5.91e-153j
0.037515528516882254084 - 8.813462099210273908e-858j 4.46e-53, 9.6e-160j
0.051403225132565666805 - 4.0173996239175224142e-859j 2.12e-55, 4.55e-162j
0.02493027546436748281 - 1.0698402079757076817e-857j 3.92e-47, 8.43e-154j
0.033556338205384878582 - 2.765884314520792113e-858j 6.48e-50, 1.39e-156j
0.037515528516882254084 - 1.5511279865983815336e-858j 2.84e-51, 6.12e-158j
0.033556338205384878582 - 2.1939172830418549937e-857j 2.87e-53, 6.16e-160j
0.035576548098969608401 + 1.3692930191519714079e-857j 6.9e-54, 1.48e-160j
0.051710272197503835747 - 3.4305632980788549578e-859j 5.08e-58, 1.09e-164j
0.035576548098969608401 + 2.0507388158400052455e-858j 1.02e-51, 2.2e-158j
0.046881013670162767433 - 4.6465818430025927179e-859j 5.61e-57, 1.21e-163j
0.051633445836520932478 + 3.6686435286577971854e-859j 5.22e-58, 1.12e-164j
0.041103830168126871883 - 3.996732376211781021e-858j 1.03e-57, 2.21e-164j
0.015643726907242433182 - 3.679640722654814061e-855j 8.52e-53, 1.83e-159j
0.0078868353061241253644 - 1.1488241308231940039e-856j 6.37e-50, 1.37e-156j
0.045628651659179967845 + 5.3602807262716811052e-859j 2.91e-57, 6.25e-164j
0.049802569941111046043 + 6.0997418918504370285e-859j 6.18e-60, 1.33e-166j
0.042734039808429155786 + 2.8128531998332633887e-858j 6.22e-59, 1.34e-165j
0.048971776673159168464 - 7.3676454301546671443e-859j 3.54e-60, 7.62e-167j
0.006646487931069068069 + 4.4424114903744052344e-855j 9.8e-54, 2.11e-160j
0.044244470683851062363 - 6.3302290210405069155e-859j 8.35e-58, 1.8e-164j
0.0132625721642480097 + 4.727736579461454869e-857j 3.71e-52, 7.98e-159j
0.022686822118922044262 + 3.8296896472522523911e-856j 6.17e-56, 1.33e-162j
0.044244470683851062363 - 2.0371308570811857669e-858j 3.22e-60, 6.93e-167j
0.050486226594183504201 - 3.3144243367094209434e-859j 6.78e-62, 1.46e-168j
0.041103830168126871883 - 9.4679851002027591311e-859j 1.12e-57, 2.4e-164j
0.049802569941111046043 + 3.4826877807417331301e-859j 1e-61, 2.15e-168j
0.051020386302719456685 + 4.5060524853829608904e-859j 2.72e-62, 5.86e-169j
0.045628651659179967845 + 1.5172090910624251654e-858j 1.45e-62, 3.12e-169j
0.050486226594183504201 - 5.1784179906660965895e-859j 1.78e-62, 3.83e-169j
0.051403225132565666805 - 3.2185406410176555037e-859j 7.79e-64, 1.68e-170j
0.047996760142147740875 + 4.1233693214933071617e-859j 3.43e-63, 7.38e-170j
0.051633445836520932478 + 3.2842607666976652668e-859j 1.23e-63, 2.65e-170j
0.047996760142147740875 + 9.1298313945239427537e-859j 2.35e-64, 5.06e-171j
0.046881013670162767433 - 1.1613145666115688875e-858j 2.03e-64, 4.36e-171j
0.02493027546436748281 - 2.0047328363793562607e-856j 4.92e-63, 1.06e-169j
0.048971776673159168464 - 3.7456010419826707834e-859j 6.93e-65, 1.48e-171j
0.051020386302719456685 + 3.2284128662944394334e-859j 4.32e-65, 9.21e-172j
0.039361386592938934917 + 5.847319753353168133e-858j 9.75e-65, 2.13e-171j

Download

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