Rule: Q[2, 10, 26, 37]

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)
0.99924495546316331898 - 5.7155320225643816245e-821j 1.71e-229, 1.71e-229j
-0.96082989829912525356 - 1.11760584926045871e-819j 6.68e-229, 6.68e-229j
-0.91729038055863927339 - 1.5460267114922867467e-831j 8.44e-230, 8.44e-230j
-0.99354542373365854873 + 3.5620095778866968538e-835j 1.63e-228, 1.63e-228j
0.93393143594529279541 - 1.1386210188514590545e-846j 1.74e-229, 1.74e-229j
0.91729038055863927339 + 5.7379858772238425761e-848j 8.46e-230, 8.46e-230j
0.98888796114118840295 + 4.7895340428776849965e-844j 1.41e-228, 1.41e-228j
-0.90030150467747382532 + 5.9732615358661749799e-847j 4.03e-230, 4.03e-230j
-0.98075725178499407913 - 1.4241238404795389013e-844j 9.99e-229, 9.99e-229j
0.99632772719624953917 + 4.263617878386817021e-853j 1.06e-228, 1.06e-228j
0.90030150467747382532 - 3.437505983923059255e-857j 4.11e-230, 4.11e-230j
-0.97097970372847336876 + 8.3194606100084959192e-854j 8.33e-229, 8.33e-229j
-0.93393143594529279541 - 1.0823102686051681386e-863j 1.76e-229, 1.76e-229j
-0.83719583016339304429 - 9.4016858649789600825e-876j 1.54e-231, 1.54e-231j
0.99354542373365854873 - 8.0896121315075017155e-877j 1.67e-228, 1.67e-228j
0.81409438324679865591 + 1.5457581697807150704e-883j 4.69e-232, 4.69e-232j
0.83719583016339304429 + 1.2952931472269034639e-881j 1.53e-231, 1.53e-231j
-0.99632772719624953917 - 8.5181679381524962215e-875j 1.1e-228, 1.1e-228j
-0.7622702556366203736 + 1.8740030879436733631e-897j 2.78e-233, 2.78e-233j
-0.88172223172009705855 - 5.8616943901785189063e-892j 1.64e-230, 1.64e-230j
0.96082989829912525356 + 7.7304960070422325937e-899j 6.5e-229, 6.5e-229j
0.73352720065312134578 + 1.2771997059181010848e-906j 5.9e-234, 5.9e-234j
-0.98888796114118840295 + 3.5914172061393274612e-899j 1.27e-228, 1.27e-228j
-0.86023849900519475227 - 1.0678276301688419306e-912j 4.61e-231, 4.61e-231j
-0.78962889608727415954 - 1.2875440683428302859e-915j 1.24e-232, 1.24e-232j
0.86023849900519475227 - 1.4327799272606293092e-913j 4.89e-231, 4.89e-231j
0.70521135282971691338 + 2.8640666576732164717e-917j 1.21e-234, 1.21e-234j
0.94890099083093036985 + 1.460860372088117955e-912j 3.7e-229, 3.7e-229j
-0.99924495546316331898 - 2.53352652244406682e-910j 1.86e-229, 1.86e-229j
-0.60984955565199760524 - 8.9115020586533473773e-926j 3.8e-237, 3.8e-237j
-0.67579359749814905043 + 4.6237312409417800705e-923j 2.05e-235, 2.05e-235j
0.7622702556366203736 - 1.9236093622247675876e-921j 2.68e-233, 2.68e-233j
0.67579359749814905043 + 4.7126006367826915349e-923j 2.14e-235, 2.14e-235j
0.97097970372847336876 + 9.9263824301273860729e-915j 8.46e-229, 8.46e-229j
-0.70521135282971691338 + 2.4605145919076036621e-926j 1.2e-234, 1.2e-234j
-0.73352720065312134578 + 2.4579948163924517125e-925j 5.46e-234, 5.46e-234j
0.50759139698158116663 - 5.0258970614514055076e-931j 6.13e-240, 6.13e-240j
0.57735026918962576451 - 1.6598837141609601127e-928j 5.47e-238, 5.47e-238j
0.78962889608727415954 + 3.0591497035936183345e-923j 1.23e-232, 1.23e-232j
-0.81409438324679865591 + 1.123986052878856003e-923j 4.73e-232, 4.73e-232j
-0.57735026918962576451 - 2.2457546570586881926e-930j 5.5e-238, 5.5e-238j
0.040648716623121461557 - 2.6865721663101388543e-945j 1.74e-254, 1.74e-254j
0.64340061993663062782 - 1.43137565037990389e-926j 2.89e-236, 2.89e-236j
0.60984955565199760524 + 1.0105334454484259598e-927j 3.76e-237, 3.76e-237j
-2.5042383679583189842e-971 - 1.0181262598183443284e-969j 7.64e-968, 7.64e-968j
-0.54401451693652160298 - 8.8488796789447057453e-931j 6.51e-239, 6.51e-239j
-0.43466256338320606749 + 2.3136293744504769991e-933j 5.64e-242, 5.64e-242j
0.28142267986093438556 - 4.118717319008275988e-939j 1.27e-246, 1.27e-246j
0.47030279866038976936 + 1.323656251733715483e-931j 5.58e-241, 5.58e-241j
0.43466256338320606749 - 8.8332754955668022639e-933j 5.34e-242, 5.34e-242j
-0.64340061993663062782 + 1.3361286627977799521e-927j 2.9e-236, 2.9e-236j
-0.50759139698158116663 - 2.3614120155985832188e-933j 6.19e-240, 6.19e-240j
0.98075725178499407913 - 6.8712814721805454407e-923j 8.89e-229, 8.89e-229j
0.88172223172009705855 - 2.5154424836960714829e-931j 1.48e-230, 1.48e-230j
0.54401451693652160298 + 1.2193072730172612276e-939j 6.99e-239, 6.99e-239j
-0.081653389898729839089 - 7.0926432527578064468e-953j 4.03e-253, 4.03e-253j
-0.47030279866038976936 - 9.7974233347400223651e-941j 5.43e-241, 5.43e-241j
-0.20213781196077181876 - 2.8349385429123181225e-949j 3.69e-249, 3.69e-249j
-0.94890099083093036985 + 7.3068598317935687262e-949j 3.32e-229, 3.32e-229j
0.39838961527322070225 + 4.9517886905179643706e-967j 4.21e-243, 4.21e-243j
0.16128546607495355561 + 8.2317701659420632809e-974j 1.65e-250, 1.65e-250j
-0.39838961527322070225 - 8.2716403356317603928e-967j 4.33e-243, 4.33e-243j
-0.35909882564439703209 + 5.9801875026361719761e-967j 2.89e-244, 2.89e-244j
0.20213781196077181876 + 2.1648924752815151768e-972j 4.13e-249, 4.13e-249j
0.35909882564439703209 - 3.8544890419587911652e-967j 2.64e-244, 2.64e-244j
0.24297054275825075281 + 1.0468434804639231084e-972j 7.8e-248, 7.8e-248j
-0.16128546607495355561 + 1.6645474226351126877e-973j 1.56e-250, 1.56e-250j
-0.31933042662507117255 - 2.3437748004654001971e-968j 1.87e-245, 1.87e-245j
-0.12172613438315505292 - 7.0116584167129822062e-975j 7.86e-252, 7.86e-252j
0.12172613438315505292 + 4.4093270375534548121e-975j 8.28e-252, 8.28e-252j
0.31933042662507117255 + 1.4033590742010145763e-968j 1.84e-245, 1.84e-245j
0.081653389898729839089 + 8.9044335463697878251e-976j 4.03e-253, 4.03e-253j
-0.24297054275825075281 + 3.9696690976225826013e-971j 7.94e-248, 7.94e-248j
-0.28142267986093438556 + 1.2306427895395117157e-969j 1.37e-246, 1.37e-246j
-0.040648716623121461557 + 5.1632928692438035072e-977j 1.74e-254, 1.74e-254j

Weights

Weight (ball center) Error (ball radius)
0.0019169492618897492117 + 9.7018388357229241489e-821j 5.27e-19, 9.01e-128j
0.010557030929193250188 - 8.9384625143813947485e-821j 2.44e-19, 4.17e-128j
0.016886342694389820958 + 3.9982890055177456727e-820j 1.76e-19, 3.01e-128j
0.0025822455981236055031 + 1.6876712644105239168e-820j 6.43e-20, 1.1e-128j
0.0161130842830981618 + 4.5711176775264968458e-821j 1.66e-20, 2.85e-129j
0.016886342694389820958 - 4.3475458393294592759e-821j 1.37e-20, 2.35e-129j
0.0067882272507883725649 - 1.337131311724139649e-820j 3.24e-21, 5.54e-130j
0.017357756827924184601 - 3.484220093048875519e-820j 2.62e-21, 4.48e-130j
0.009212635855320633703 + 3.113994367637980491e-820j 1.1e-21, 1.88e-130j
0.0034906943150965840831 - 2.4261611923096771254e-820j 2.46e-21, 4.21e-130j
0.017357756827924184601 + 4.1677916626807031649e-821j 2.42e-22, 4.14e-131j
0.010055784943015079899 - 8.8165956993337722162e-820j 1.01e-21, 1.72e-130j
0.0161130842830981618 - 5.2006356191351622328e-820j 5.48e-22, 9.38e-131j
0.023158022302295188172 + 2.3873968392975003759e-820j 2.69e-24, 4.61e-133j
0.0025822455981236055031 + 2.3564974951616166644e-820j 1.25e-21, 2.14e-130j
0.023319738153612729786 + 2.740939352492836633e-821j 3.8e-25, 6.51e-134j
0.023158022302295188172 - 2.9086807555501585296e-821j 7.65e-25, 1.31e-133j
0.0034906943150965840831 - 8.1515963558613180331e-821j 8.77e-24, 1.5e-132j
0.028458786114830847268 - 2.0244045013860715673e-820j 7.37e-27, 1.26e-135j
0.020080313024541400358 + 2.8783374317591162399e-820j 1.62e-24, 2.77e-133j
0.010557030929193250188 + 6.9771571928911810106e-821j 2.56e-26, 4.38e-135j
0.028641438580198807115 - 1.6665060754722412958e-821j 5.09e-29, 8.7e-138j
0.0067882272507883725649 - 2.0479543951850574411e-820j 1.14e-23, 1.95e-132j
0.022607932836731709954 - 2.4527760728085017339e-820j 3.55e-25, 6.08e-134j
0.025944115451340669117 + 2.1821246788093109874e-820j 4.53e-27, 7.74e-136j
0.022607932836731709954 + 3.0731750324387097839e-821j 8.56e-28, 1.46e-136j
0.028309133270025383483 + 1.3818052903339028705e-821j 2.24e-30, 3.84e-139j
0.013548823444910203366 - 5.6290740600580757166e-821j 4.88e-27, 8.36e-136j
0.0019169492618897492117 + 1.1594348897585111057e-821j 1.09e-25, 1.87e-134j
0.033162973724487790592 + 2.0895647410618360161e-820j 1.66e-32, 2.84e-141j
0.030937836054740270047 + 2.0647286370663366244e-820j 1.8e-31, 3.08e-140j
0.028458786114830847268 + 1.9129061468816593797e-821j 9.89e-31, 1.69e-139j
0.030937836054740270047 - 9.4070302067102376745e-822j 1.81e-32, 3.09e-141j
0.010055784943015079899 - 7.3523979910986581367e-821j 1e-28, 1.71e-137j
0.028309133270025383483 - 2.1656664190454474931e-820j 1.3e-31, 2.22e-140j
0.028641438580198807115 + 2.0866725327492085961e-820j 3.91e-31, 6.69e-140j
0.037442017126466574908 - 1.7916230198265507342e-821j 2.02e-36, 3.46e-145j
0.032230256054342294124 - 5.8058403336798463098e-822j 1.58e-35, 2.7e-144j
0.025944115451340669117 - 2.3257503444829364485e-821j 1.69e-31, 2.89e-140j
0.023319738153612729786 - 2.3727373647509548472e-820j 5.85e-31, 1e-139j
0.032230256054342294124 - 2.2135037942898687578e-820j 4.92e-36, 8.41e-145j
0.040954890594717094903 - 1.6140926202146246802e-820j 4.11e-41, 7.04e-150j
0.033467871097178098669 + 4.6856320833619658645e-822j 6.7e-35, 1.15e-143j
0.033162973724487790592 + 1.503914061416367012e-823j 1.43e-35, 2.44e-144j
0.040449427712190875964 + 1.7426719048782686707e-820j 1.27e-41, 2.18e-150j
0.034935506089723814378 + 2.1329306911030760911e-820j 1.46e-38, 2.5e-147j
0.035170876295424463479 - 2.3260240157084794207e-820j 7.84e-41, 1.34e-149j
0.037467616898532022717 - 8.4139960206036477492e-821j 2.07e-42, 3.54e-151j
0.036597372781257761127 + 2.7101619386848093138e-821j 2.9e-40, 4.96e-149j
0.035170876295424463479 - 3.7527495587645520819e-821j 4.88e-41, 8.36e-150j
0.033467871097178098669 - 1.9735978435850648662e-820j 1.23e-38, 2.1e-147j
0.037442017126466574908 - 2.0522856096318874302e-820j 3.27e-41, 5.6e-150j
0.009212635855320633703 + 7.9564827864512865865e-821j 2.07e-37, 3.54e-146j
0.020080313024541400358 - 3.590226546986281296e-821j 1.72e-37, 2.95e-146j
0.034935506089723814378 + 1.1582767960903481266e-821j 3.96e-40, 6.78e-149j
0.040753601602131276817 + 1.97634981235039169e-820j 1.46e-46, 2.5e-155j
0.036597372781257761127 + 2.1899455234275843732e-820j 2.02e-43, 3.46e-152j
0.041332266702228839662 - 2.0987104881952738041e-820j 3.29e-47, 5.63e-156j
0.013548823444910203366 + 1.0743129736701368283e-819j 2.34e-40, 4e-149j
0.037891641353203400032 + 4.5242713148349573735e-821j 1.66e-44, 2.84e-153j
0.040096448488875206028 + 1.2136393635380506444e-820j 2.51e-47, 4.29e-156j
0.037891641353203400032 + 2.2332305803560462014e-820j 7.97e-46, 1.36e-154j
0.04014750615507154346 - 2.1341851770667431388e-820j 9.57e-47, 1.64e-155j
0.041332266702228839662 - 1.0373439416175543967e-820j 6.28e-48, 1.08e-156j
0.04014750615507154346 - 5.3576543059397003786e-821j 4.46e-47, 7.63e-156j
0.03981777970852427846 + 9.3719576647139805162e-821j 7.48e-48, 1.28e-156j
0.040096448488875206028 + 2.1123812252172828557e-820j 5.07e-50, 8.68e-159j
0.038886650785604492348 + 2.242949803897692503e-820j 9.32e-50, 1.59e-158j
0.039453119494068959137 - 2.0992252023485830631e-820j 4e-50, 6.86e-159j
0.039453119494068959137 - 1.3877585420698947793e-820j 2.53e-50, 4.32e-159j
0.038886650785604492348 + 6.8305002023302419863e-821j 1.27e-49, 2.17e-158j
0.040753601602131276817 + 1.5003476108713823671e-820j 1.23e-50, 2.1e-159j
0.03981777970852427846 + 2.2208637697884456196e-820j 1.75e-51, 2.94e-160j
0.037467616898532022717 - 2.3358303879782585231e-820j 1.75e-51, 2.91e-160j
0.040954890594717094903 - 1.8502635932057648274e-820j 1.72e-51, 3.1e-160j

Download

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