Rule: Q[3, 10, 14, 28]

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.

Warning: This rule has negative weights!

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)
-0.99696345573553342034 - 1.7133706256683044248e-851j 2.69e-236, 2.69e-236j
-0.98189373966174310941 - 5.5781682594312115581e-851j 2.04e-236, 2.04e-236j
-0.93054609618299054922 - 8.9329784724154089439e-852j 2.93e-237, 2.93e-237j
0.99953206505353089654 - 1.242996227287699039e-848j 1.28e-236, 1.28e-236j
0.95151371618655174505 - 4.42244294541426264e-861j 6.48e-237, 6.48e-237j
0.93054609618299054922 + 8.8962852014686948872e-871j 2.81e-237, 2.81e-237j
-0.99125588906108358532 + 9.133752471811688325e-884j 2.75e-236, 2.75e-236j
-0.90591989788431806766 - 9.2526687193351997695e-887j 1.12e-237, 1.12e-237j
0.99125588906108358532 + 3.7490284527737624971e-883j 2.79e-236, 2.79e-236j
0.99696345573553342034 - 1.1428885680495191709e-897j 2.72e-236, 2.72e-236j
0.90591989788431806766 + 1.0080084284612028108e-907j 1.12e-237, 1.12e-237j
0.64533232741799124195 - 1.2507811206058916662e-919j 3.92e-242, 3.92e-242j
-0.87783567338819181439 + 1.8510276072783735115e-915j 3.87e-238, 3.87e-238j
-0.84648809715906767396 - 1.5778796718624308843e-916j 1.22e-238, 1.22e-238j
-0.99953206505353089654 + 4.5190793601052618905e-914j 1.19e-236, 1.19e-236j
0.81203591675445274504 - 1.3352752986760612941e-915j 3.11e-239, 3.11e-239j
0.84648809715906767396 - 7.0390662180457096177e-914j 1.24e-238, 1.24e-238j
-0.95151371618655174505 + 2.5019488731398063576e-916j 6.52e-237, 6.52e-237j
-0.81203591675445274504 + 8.0180531029613210473e-922j 3.22e-239, 3.22e-239j
-0.96865830675279425645 - 5.3865018285478620752e-918j 1.16e-236, 1.16e-236j
0.87783567338819181439 + 1.6180998407882068217e-916j 3.9e-238, 3.9e-238j
0.77459666924148337704 + 3.3896614843158326624e-926j 7.43e-240, 7.43e-240j
-0.17101852249474448773 + 2.524944194447553184e-938j 7e-251, 7e-251j
-0.73426377039106497216 - 1.5406556471518170923e-935j 1.68e-240, 1.68e-240j
-0.69113262396834268581 + 1.6351547966143473323e-936j 2.57e-241, 2.57e-241j
0.98189373966174310941 + 1.7507994279759251595e-936j 2.13e-236, 2.13e-236j
0.73426377039106497216 + 1.3666042051371234735e-958j 1.52e-240, 1.52e-240j
0.54665888028373232627 + 4.6198224994152323316e-965j 5.75e-244, 5.75e-244j
-0.14715303420776064898 - 2.9293716073366541031e-971j 2.51e-251, 2.51e-251j
-0.64533232741799124195 - 2.2223599512829202247e-965j 3.8e-242, 3.8e-242j
-0.77459666924148337704 - 2.8420454492511695966e-962j 7.67e-240, 7.67e-240j
0.22617367918814454639 - 4.1074413340717849925e-972j 3.95e-250, 3.95e-250j
0.69113262396834268581 - 1.1101845996015812143e-964j 2.6e-241, 2.6e-241j
0.96865830675279425645 + 4.3509999194424858363e-972j 1.24e-236, 1.24e-236j
-0.59706738604131558719 + 4.1670609696143649089e-984j 4.84e-243, 4.84e-243j
-0.49455577980099296881 + 2.4781143829813209583e-986j 6.3e-245, 6.3e-245j
0.060379947809744553847 - 4.4227439116404375672e-996j 2.75e-254, 2.75e-254j
0.59706738604131558719 + 1.6114162998469263714e-987j 4.98e-243, 4.98e-243j
0.17101852249474448773 + 1.0992542393591864204e-994j 7.01e-251, 7.01e-251j
-0.33324545045981175859 + 2.0711178466396034129e-990j 4.44e-248, 4.44e-248j
-0.54665888028373232627 - 2.3265110498840174026e-989j 5.87e-244, 5.87e-244j
-0.12051321105334727754 + 6.047636173287535422e-999j 3.24e-252, 3.24e-252j
0.38736385932378655649 + 1.0486361742793682567e-992j 5.46e-247, 5.46e-247j
0.44128701576964658439 + 2.4201576687020033041e-990j 5.8e-246, 5.8e-246j
9.6248242866313744607e-1012 - 2.4098729904223726853e-1011j 1.43e-1009, 1.43e-1009j
-0.44128701576964658439 + 2.3637767131150514222e-992j 6.23e-246, 6.23e-246j
-0.27944386352261028131 - 5.4073049719627873043e-995j 4.58e-249, 4.58e-249j
0.14715303420776064898 - 2.6353454254285993608e-997j 2.58e-251, 2.58e-251j
0.49455577980099296881 + 6.9256871551838476479e-991j 6.54e-245, 6.54e-245j
0.12051321105334727754 - 2.8703558294060407348e-999j 3.13e-252, 3.13e-252j
-0.22617367918814454639 + 1.1546183451839788659e-996j 3.94e-250, 3.94e-250j
-0.38736385932378655649 - 2.6580417805401023404e-993j 5.35e-247, 5.35e-247j
-0.060379947809744553847 - 4.0355032893887915212e-1001j 2.75e-254, 2.75e-254j
0.33324545045981175859 + 3.5223019119149691048e-994j 4.93e-248, 4.93e-248j
0.27944386352261028131 + 2.8963354945406480107e-995j 4.16e-249, 4.16e-249j

Weights

Weight (ball center) Error (ball radius)
0.0040176984325220973381 + 8.2847210887463102721e-852j 1.72e-51, 3.18e-165j
0.011280115131044668763 - 2.9089989321611296657e-851j 1.01e-51, 1.87e-165j
0.022828774477648776837 + 4.7660484685893942088e-851j 5.05e-52, 9.37e-166j
0.0012937720931858497773 + 1.152681806621583363e-848j 3.29e-53, 6.09e-167j
0.019078356223886945489 - 1.2052791968632901442e-849j 1.88e-53, 3.48e-167j
0.022828774477648776837 + 8.9938440694486500083e-850j 1.23e-53, 2.28e-167j
0.0074789788411870403592 - 1.9551878072837634339e-851j 1.13e-52, 2.09e-166j
0.026389464745564009762 - 3.8689151066374859674e-851j 3.95e-54, 7.33e-168j
0.0074789788411870403592 + 6.1796401285830488957e-849j 7.25e-54, 1.34e-167j
0.0040176984325220973381 - 1.5727854470036222873e-848j 1.54e-53, 2.85e-167j
0.026389464745564009762 - 7.3512080685180959689e-850j 4.07e-55, 7.55e-169j
0.047075295862928102142 + 7.5384922486591921237e-850j 1.59e-57, 2.95e-171j
0.029745997640958017509 + 4.6846420208727718781e-851j 1.4e-55, 2.59e-169j
0.032922616047535359317 - 5.5155809166450507421e-851j 2.62e-56, 4.87e-170j
0.0012937720931858497773 - 1.2418959795829463392e-851j 1.1e-54, 2.05e-168j
0.035962485037455604115 + 5.8543654206900428368e-850j 5.23e-58, 9.69e-172j
0.032922616047535359317 - 6.0168672187890902885e-850j 1.18e-57, 2.18e-171j
0.019078356223886945489 - 6.2962025742847588981e-851j 7e-56, 1.3e-169j
0.035962485037455604115 + 6.5976119596656805316e-851j 1.24e-58, 2.3e-172j
0.015195780912532016749 + 8.517398540219664555e-851j 1.14e-55, 2.1e-169j
0.029745997640958017509 + 6.4639699201321084752e-850j 1.15e-58, 2.14e-172j
0.038900882893046102933 - 5.9078727372194304224e-850j 5.15e-60, 9.55e-174j
0.060894698215360563257 - 5.7119126156688246955e-848j 7.37e-64, 1.37e-177j
0.041749518179243502306 + 1.0018166136162407512e-850j 5.25e-61, 9.74e-175j
0.044491977950426821612 - 1.2805720822158630712e-850j 1.05e-61, 1.95e-175j
0.011280115131044668763 - 3.0798203989370156794e-849j 1.03e-59, 1.91e-173j
0.041749518179243502306 + 6.1674286852663868254e-850j 6.84e-62, 1.27e-175j
0.051340056238131434229 + 1.1315154662224027282e-849j 2.56e-64, 4.75e-178j
-0.014690263023767041262 + 9.5198125895388157501e-848j 2.79e-65, 5.18e-179j
0.047075295862928102142 + 1.6937335851022463585e-850j 1.13e-63, 2.09e-177j
0.038900882893046102933 - 8.0444525226010466122e-851j 1.04e-61, 1.92e-175j
0.053327686562126791939 + 2.0137867218886586619e-848j 1.57e-67, 2.91e-181j
0.044491977950426821612 - 6.6754375033597231059e-850j 9.21e-64, 1.71e-177j
0.015195780912532016749 + 1.8036633335596769501e-849j 8.18e-62, 1.52e-175j
0.049401342762070116204 - 2.341421177003366438e-850j 3.04e-65, 5.64e-179j
0.052776089641081016622 - 5.2938344715428381243e-850j 8.52e-67, 1.58e-180j
0.060019929418447012772 + 2.3389316854826229244e-848j 6.68e-69, 1.24e-182j
0.049401342762070116204 - 8.9613341669084223628e-850j 1.96e-66, 3.63e-180j
0.060894698215360563257 - 8.0141913336376009857e-848j 8e-69, 1.48e-182j
0.05405213283963196628 + 2.8491982931359818303e-849j 3.73e-69, 6.91e-183j
0.051340056238131434229 + 3.416064072872414043e-850j 2.58e-67, 4.79e-181j
0.0629241968468818835 - 5.9309846297662179605e-848j 1.1e-68, 2.04e-182j
0.054097562070695104487 - 3.4014435369628837284e-849j 2.37e-70, 4.39e-184j
0.053675151383444314146 + 2.2045873996360485834e-849j 3.72e-70, 6.9e-184j
0.060574547817963754384 - 1.7555089600413229612e-848j 2.6e-70, 4.83e-184j
0.053675151383444314146 + 8.7266667666199970335e-850j 3.34e-70, 6.2e-184j
0.053482428667750045627 - 5.6989682454585851059e-849j 1.57e-70, 2.91e-184j
-0.014690263023767041262 + 1.2731138498864064009e-847j 9.29e-71, 1.72e-184j
0.052776089641081016622 - 1.5268282040016166315e-849j 7.64e-72, 1.42e-185j
0.0629241968468818835 - 7.5209396809344995008e-848j 5.47e-71, 1.01e-184j
0.053327686562126791939 + 1.2825695997519216987e-848j 1.36e-71, 2.53e-185j
0.054097562070695104487 - 1.5284329764958227305e-849j 3.2e-72, 5.94e-186j
0.060019929418447012772 + 2.0774030258032242151e-848j 6.51e-72, 1.21e-185j
0.05405213283963196628 + 5.616017816277630191e-849j 7.6e-74, 1.41e-187j
0.053482428667750045627 - 1.0002275275958901947e-848j 1.47e-73, 2.72e-187j

Download

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