Rule: Q[4, 10, 16, 26]

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)
-0.68434439617662082055 - 2.4273832956408671981e-859j 1.3e-240, 1.3e-240j
0.99846408876102889709 - 8.0667239585649416048e-852j 5.14e-236, 5.14e-236j
-0.96426964940448726751 + 4.1444850945555838079e-865j 1.36e-235, 1.36e-235j
0.99444997880691468328 + 1.9946264297286929136e-868j 2.7e-235, 2.7e-235j
0.93807933324805675366 - 1.9932853214408603114e-876j 5.77e-236, 5.77e-236j
0.95280406968027788258 + 2.6154914125000660757e-879j 1.27e-235, 1.27e-235j
-0.979984994846605313 + 8.3691190979770759464e-885j 1.16e-235, 1.16e-235j
-0.88565589101360055815 + 5.2645209687748220862e-897j 6.76e-237, 6.76e-237j
-0.99444997880691468328 + 1.0937299255959162597e-897j 2.48e-235, 2.48e-235j
0.99159141688616824102 + 7.5077228797666694406e-910j 2.9e-235, 2.9e-235j
0.86113631159405257522 + 2.0866956224661052513e-915j 2.78e-237, 2.78e-237j
-0.99846408876102889709 - 1.8042492155816789262e-913j 5.36e-236, 5.36e-236j
-0.93807933324805675366 - 3.6366193533646857679e-924j 5.62e-236, 5.62e-236j
-0.86113631159405257522 + 1.9087131446271833791e-937j 2.76e-237, 2.76e-237j
0.9130922314964186299 + 3.3362395242522183347e-937j 1.56e-236, 1.56e-236j
0.83337192759012916111 - 9.0454210741146749426e-939j 8.33e-238, 8.33e-238j
0.88565589101360055815 + 5.5061769888622788153e-938j 6.54e-237, 6.54e-237j
-0.95280406968027788258 + 1.6792231438515900336e-935j 1.27e-235, 1.27e-235j
-0.75935800346489474102 - 2.3495984918148571004e-945j 3.55e-239, 3.55e-239j
-0.4988494585210985124 - 2.1109990402148881214e-950j 2.09e-244, 2.09e-244j
0.979984994846605313 - 2.4069425166081789331e-939j 1.24e-235, 1.24e-235j
0.72317255923281838433 - 1.7938944012629465015e-955j 7.76e-240, 7.76e-240j
-0.9130922314964186299 - 6.743834066999894872e-952j 1.78e-236, 1.78e-236j
-0.83337192759012916111 + 1.0815119727046925714e-957j 7.62e-238, 7.62e-238j
-0.79754531704369287258 + 1.8879711041009089735e-959j 1.58e-238, 1.58e-238j
0.22923147134799356198 + 7.3036574538035706477e-970j 1.84e-250, 1.84e-250j
0.75935800346489474102 - 1.3329846227327973206e-957j 3.49e-239, 3.49e-239j
0.79754531704369287258 + 3.1762251934820640542e-956j 1.53e-238, 1.53e-238j
0.96426964940448726751 - 6.6509799213992176786e-958j 1.37e-235, 1.37e-235j
-0.63903634397661954543 + 1.2868476804458779552e-973j 1.41e-241, 1.41e-241j
-0.99159141688616824102 - 3.1912748614291546398e-976j 2.88e-235, 2.88e-235j
0.68434439617662082055 - 9.287157670080924021e-983j 1.19e-240, 1.19e-240j
0.63903634397661954543 + 3.2454193078472247748e-985j 1.44e-241, 1.44e-241j
0.059395083952110442815 - 5.339502855335518729e-997j 2.42e-254, 2.42e-254j
-0.54627694908708365616 + 4.4105904008434852457e-986j 2.29e-243, 2.29e-243j
-0.72317255923281838433 + 1.9694704000765660599e-986j 7.68e-240, 7.68e-240j
0.00081650472666657241228 + 5.8048008317375478494e-1003j 1.27e-256, 1.27e-256j
0.59174565348149751694 + 1.5899670920068510468e-988j 1.77e-242, 1.77e-242j
0.39201974019645042693 - 3.7707189324382358281e-994j 1.02e-246, 1.02e-246j
-0.3399810435848562648 + 7.6600811455611387621e-994j 7.1e-248, 7.1e-248j
-0.59174565348149751694 + 5.3079542323483707268e-994j 1.74e-242, 1.74e-242j
-0.17099452449708508805 + 1.245739197164502995e-1001j 9.73e-252, 9.73e-252j
0.44614207406094625197 - 1.979689516977339546e-992j 1.55e-245, 1.55e-245j
0.54627694908708365616 - 1.3890586594871305353e-991j 2.15e-243, 2.15e-243j
-0.11539569344883949077 - 4.6345870098845823942e-1003j 5.93e-253, 5.93e-253j
-0.44614207406094625197 + 3.2921392576775405046e-996j 1.5e-245, 1.5e-245j
-0.28673611026301184315 - 4.3779095270078917701e-1000j 4.42e-249, 4.42e-249j
0.11539569344883949077 + 4.7286071555741002028e-1004j 4.48e-253, 4.48e-253j
0.4988494585210985124 - 5.4244166806351092295e-994j 1.99e-244, 1.99e-244j
0.17099452449708508805 - 3.5046552054510724456e-1002j 8.76e-252, 8.76e-252j
-0.22923147134799356198 - 1.5841818376958569375e-1001j 1.95e-250, 1.95e-250j
-0.39201974019645042693 - 9.9658644217423054192e-998j 1.06e-246, 1.06e-246j
-0.059395083952110442815 + 6.7653328043400305364e-1005j 2.42e-254, 2.42e-254j
0.3399810435848562648 - 2.1610202361309305816e-997j 7.49e-248, 7.49e-248j
0.28673611026301184315 + 6.5885304407776590203e-1001j 4.09e-249, 4.09e-249j
-0.00081650472666657241228 - 2.0011956123199694606e-1007j 1.27e-256, 1.27e-256j

Weights

Weight (ball center) Error (ball radius)
0.042445870481232770006 - 3.2903350370705661755e-853j 7.76e-49, 3.01e-161j
0.0039129690387511970721 + 1.9124379449402724486e-851j 3.71e-49, 1.44e-161j
0.016174672578068093424 - 1.6782142405434877093e-853j 3.57e-50, 1.38e-162j
0.00066148600709035689333 - 4.6178398883184372135e-851j 3.01e-49, 1.17e-161j
0.02188144324578370543 + 6.4527181785163369008e-852j 2.66e-50, 1.03e-162j
0.0081057528157774294064 - 1.060529661117996509e-851j 3.68e-50, 1.43e-162j
0.014070265958212799173 + 7.8098197335462662919e-854j 1.29e-51, 4.99e-164j
0.026610557022868523129 - 2.1266452959948128235e-853j 3.76e-52, 1.46e-164j
0.00066148600709035689333 + 9.3012112997578064648e-854j 2.08e-52, 8.06e-165j
0.0087798658924361326603 + 3.1892967699503102832e-851j 3.17e-51, 1.23e-163j
0.023810936262424228652 - 3.5576859778355963145e-852j 9.3e-54, 3.6e-166j
0.0039129690387511970721 - 1.5806696362640972349e-854j 1.1e-52, 4.28e-165j
0.02188144324578370543 - 2.0120682529911812439e-853j 2.83e-53, 1.1e-165j
0.023810936262424228652 + 2.6272795524545146865e-853j 6.08e-54, 2.36e-166j
0.027090130380102171782 - 3.5773435109978379994e-852j 4.97e-54, 1.92e-166j
0.032543493401351259656 + 2.7125361468201227689e-852j 1.31e-55, 5.06e-168j
0.026610557022868523129 + 3.5519188102150455977e-852j 1.77e-54, 6.85e-167j
0.0081057528157774294064 + 2.4816577761623524151e-853j 3.75e-54, 1.45e-166j
0.037429984737186386358 - 2.776700259069575769e-853j 2.11e-57, 8.17e-170j
0.050308205002836370701 - 5.1295562442465864447e-853j 1.01e-59, 3.9e-172j
0.014070265958212799173 - 8.3615206967259358227e-852j 3.97e-55, 1.54e-167j
0.035970977520316688548 - 2.0477779195504179796e-852j 5.26e-59, 2.04e-171j
0.027090130380102171782 + 1.5976741494703280849e-853j 1.31e-55, 5.08e-168j
0.032543493401351259656 - 2.4446421371800578297e-853j 6.02e-57, 2.33e-169j
0.038013118214518050793 + 2.3042070068317760847e-853j 1.47e-57, 5.71e-170j
0.058716149929766065191 - 2.0880714382615602419e-852j 5.35e-64, 2.07e-176j
0.037429984737186386358 + 2.0413312342949885245e-852j 1.11e-60, 4.31e-173j
0.038013118214518050793 - 2.0597272489900562454e-852j 3.85e-60, 1.49e-172j
0.016174672578068093424 + 9.6328180920921740168e-852j 3.51e-58, 1.36e-170j
0.04724564626201925455 + 3.3635760590952963086e-853j 1.01e-62, 3.89e-175j
0.0087798658924361326603 - 1.1014259404222419682e-853j 1.14e-58, 4.42e-171j
0.042445870481232770006 + 1.7627052598599419893e-852j 8.47e-63, 3.28e-175j
0.04724564626201925455 - 1.5323952187706527844e-852j 6.26e-64, 2.43e-176j
0.057829480993054206343 + 6.9312518951355437456e-852j 5.26e-68, 2.04e-180j
0.045236716024135503558 + 4.7903492056917099692e-853j 2.4e-65, 9.28e-178j
0.035970977520316688548 + 3.274415940713514113e-853j 7.02e-63, 2.72e-175j
0.030126785352777760943 - 2.2702709980445303801e-850j 2.43e-68, 9.43e-181j
0.04653141982308142313 + 1.5743514942351095481e-852j 5.7e-66, 2.21e-178j
0.053209418028393411724 + 1.6127371759527996355e-852j 3.69e-68, 1.43e-180j
0.051586332116072347896 + 8.861449864124361276e-853j 1.01e-68, 3.93e-181j
0.04653141982308142313 - 4.0266259231481801201e-853j 8.2e-66, 3.18e-178j
0.057048748589480409853 - 1.929814853679314627e-852j 1.63e-69, 6.32e-182j
0.054298416204095387754 - 1.4724646656322116897e-852j 8.93e-69, 3.46e-181j
0.045236716024135503558 - 1.6364568702685200194e-852j 6.72e-68, 2.6e-180j
0.054808817968806649341 + 3.1375298212063198495e-852j 5.35e-70, 2.07e-182j
0.054298416204095387754 + 5.629733251950350008e-853j 4.81e-69, 1.86e-181j
0.055552340149361416032 - 1.046247729812454021e-852j 4.81e-70, 1.86e-182j
0.054808817968806649341 - 3.9575283708156454082e-852j 4.26e-71, 1.65e-183j
0.050308205002836370701 + 1.5372954469072135563e-852j 1.83e-70, 7.03e-183j
0.057048748589480409853 + 2.7273976531018642214e-852j 2.08e-71, 8.08e-184j
0.058716149929766065191 + 1.3083151600844117089e-852j 2.66e-71, 1.03e-183j
0.053209418028393411724 - 7.0337777543470816594e-853j 4.5e-71, 1.73e-183j
0.057829480993054206343 - 6.1529209551035968006e-852j 8.21e-72, 3.17e-184j
0.051586332116072347896 - 1.8011950052661551541e-852j 8.88e-73, 3.11e-185j
0.055552340149361416032 + 1.8892579309353101979e-852j 7.96e-73, 2.71e-185j
0.030126785352777760943 + 2.2665609552614587789e-850j 7.48e-71, 3.51e-183j

Download

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