Rule: Q[7, 30, 38]

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)
0.99964153853917963513 - 3.0335516469500603131e-1713j 2.95e-484, 2.95e-484j
-0.94910791234275852453 + 1.5777226007763999709e-1727j 3.56e-484, 3.56e-484j
-0.93498103642239154162 + 2.2985936259773936355e-1730j 1.97e-484, 1.97e-484j
-0.99784612344852210871 + 1.3931815263946779775e-1727j 8.49e-484, 8.49e-484j
0.90203388458741291848 - 5.872964013304781442e-1728j 4.37e-485, 4.37e-485j
0.91927944102079721186 - 9.8399398537013304732e-1740j 9.56e-485, 9.56e-485j
0.98868775153792583362 + 6.6122740208315655137e-1762j 1.21e-483, 1.21e-483j
-0.91927944102079721186 - 6.4424176456842695408e-1789j 9.38e-485, 9.38e-485j
-0.98139085440145282256 + 4.0404285326095066328e-1787j 1.02e-483, 1.02e-483j
-0.99964153853917963513 + 4.3968572669906030663e-1786j 2.96e-484, 2.96e-484j
0.8832767929424487679 - 1.512316434375854922e-1790j 1.77e-485, 1.77e-485j
0.99784612344852210871 + 5.0661869553378524444e-1816j 8.57e-484, 8.57e-484j
-0.8832767929424487679 - 1.5083788495341239413e-1851j 1.73e-485, 1.73e-485j
-0.86307451812359299498 + 9.9099856251806756322e-1854j 6.42e-486, 6.42e-486j
0.98139085440145282256 + 7.6964637924286665188e-1850j 1.09e-483, 1.09e-483j
0.86307451812359299498 + 4.2263617437314404434e-1865j 6.25e-486, 6.25e-486j
0.79418608920443608857 - 2.2591484597239407029e-1869j 1.65e-487, 1.65e-487j
-0.98868775153792583362 - 9.6265178228632329426e-1864j 1.16e-483, 1.16e-483j
-0.79418608920443608857 + 3.3770573443257970953e-1870j 1.66e-487, 1.66e-487j
-0.96159125459099586695 + 1.069030758985076518e-1864j 5.48e-484, 5.48e-484j
0.93498103642239154162 + 6.1781432516485382848e-1866j 1.9e-484, 1.9e-484j
0.6836267794908846579 + 8.8117971691939698892e-1886j 2.33e-490, 2.33e-490j
-0.994202017165507384 - 5.0443979168474030869e-1878j 1.1e-483, 1.1e-483j
-0.84148519136966672985 + 9.2735449259205515255e-1883j 2.1e-486, 2.1e-486j
-0.76851400329291491016 + 2.5261301573742106833e-1884j 4.23e-488, 4.23e-488j
0.994202017165507384 + 1.4006083453545894778e-1877j 1.06e-483, 1.06e-483j
0.76851400329291491016 + 2.0709908944012728454e-1897j 3.97e-488, 3.97e-488j
0.84148519136966672985 + 1.532874368980997699e-1895j 2.09e-486, 2.09e-486j
-0.97235933101661391008 + 4.2095708217568582956e-1893j 8.52e-484, 8.52e-484j
-0.65275488458376128405 - 8.2077486005766907041e-1901j 3.51e-491, 3.51e-491j
-0.81852084172440107155 + 1.5693657891233434075e-1898j 6.1e-487, 6.1e-487j
0.81852084172440107155 - 1.2309336348723254387e-1895j 6.22e-487, 6.22e-487j
0.74153118559939443986 - 6.0174287306988313786e-1898j 7.44e-489, 7.44e-489j
0.97235933101661391008 - 4.4459886884069155743e-1891j 8.51e-484, 8.51e-484j
-0.6836267794908846579 + 3.4887074214373528851e-1912j 2.27e-490, 2.27e-490j
-0.71323338896140600261 + 4.4883072655217794743e-1913j 1.44e-489, 1.44e-489j
0.96159125459099586695 + 1.7139210158324276115e-1904j 5.85e-484, 5.85e-484j
0.65275488458376128405 + 7.8390587941510026858e-1936j 3.37e-491, 3.37e-491j
0.94910791234275852453 - 4.0682314855606336554e-1932j 3.86e-484, 3.86e-484j
-0.74153118559939443986 + 2.6958137225920700995e-1956j 7.67e-489, 7.67e-489j
-0.55301677795294993595 - 5.7541694309521588081e-1962j 5.66e-494, 5.66e-494j
-0.90203388458741291848 + 3.7780460220364930802e-1963j 4.49e-485, 4.49e-485j
0.58740451714137191543 - 7.5424046025372422149e-1970j 5.18e-493, 5.18e-493j
0.55301677795294993595 + 1.9448285988995243863e-1971j 5.89e-494, 5.89e-494j
0.62066801549804592241 + 2.6809475561046494673e-1968j 4.52e-492, 4.52e-492j
-0.58740451714137191543 - 3.5817536924202506272e-1972j 5.22e-493, 5.22e-493j
-0.62066801549804592241 - 1.5970822016590801258e-1972j 4.6e-492, 4.6e-492j
0.71323338896140600261 - 1.8946742805727171758e-1977j 1.41e-489, 1.41e-489j
0.51758562187726784074 - 1.6074129510602532591e-1984j 5.62e-495, 5.62e-495j
0.20662717414130210908 + 2.7132217658805492039e-1994j 2e-504, 2e-504j
-0.51758562187726784074 + 1.8989001558585827909e-1983j 5.27e-495, 5.27e-495j
-0.48119644370188802369 + 4.1484127610993116179e-1986j 5.03e-496, 5.03e-496j
-0.12438944276720320083 - 2.0561488039634593745e-1997j 5.55e-507, 5.55e-507j
0.44392316342065541073 + 6.8493284219052851107e-1987j 3.99e-497, 3.99e-497j
0.48119644370188802369 - 5.4318833348886630399e-1987j 5.11e-496, 5.11e-496j
2.3870215619698884501e-2016 + 6.1772779976026846437e-2017j 1.85e-2014, 1.85e-2014j
-0.40584515137739716691 - 4.7372138246254358544e-1988j 2.91e-498, 2.91e-498j
-0.44392316342065541073 + 4.3962566387921025019e-1987j 3.72e-497, 3.72e-497j
0.24736277927426844744 + 2.5286780891386647849e-1994j 3.99e-503, 3.99e-503j
0.40584515137739716691 - 7.6492386473503533015e-1990j 2.99e-498, 2.99e-498j
0.041521319845574659748 + 3.9355238097375855915e-2000j 9.08e-510, 9.08e-510j
-0.16561533960274229959 + 7.6553516036452959336e-1996j 1.09e-505, 1.09e-505j
-0.36705948753898270572 + 4.9524583358867228056e-1989j 1.99e-499, 1.99e-499j
-0.041521319845574659748 - 6.621544049412136798e-2000j 9.08e-510, 9.08e-510j
0.32766326206750472751 - 5.3691371795717127444e-1991j 1.26e-500, 1.26e-500j
0.28773799695667453611 + 3.98166897458009894e-1992j 7.81e-502, 7.81e-502j
-0.083003770784361174585 - 3.3028500428884339138e-1999j 2.4e-508, 2.4e-508j
-0.32766326206750472751 - 1.084783469312298228e-1990j 1.17e-500, 1.17e-500j
-0.20662717414130210908 - 3.6525235568673296844e-1995j 2.04e-504, 2.04e-504j
0.16561533960274229959 + 1.1443284889186004498e-1997j 1.01e-505, 1.01e-505j
0.36705948753898270572 - 5.325428185934275176e-1990j 2.35e-499, 2.35e-499j
0.12438944276720320083 + 6.8971948998282720593e-1998j 5.95e-507, 5.95e-507j
-0.24736277927426844744 - 3.2211733606781339678e-1994j 4.23e-503, 4.23e-503j
-0.28773799695667453611 + 7.6127000750575886215e-1992j 6.84e-502, 6.84e-502j
0.083003770784361174585 - 4.3461547160766432035e-1999j 2.27e-508, 2.27e-508j

Weights

Weight (ball center) Error (ball radius)
0.0009644786972996856751 + 3.2443423417735922209e-1713j 6.38e-144, 9.68e-379j
0.013319182623224480414 - 2.7572852367191819012e-1715j 3.1e-144, 4.71e-379j
0.014922316674705628567 + 3.3513900531375489466e-1715j 2.8e-144, 4.25e-379j
0.0026939324381584941423 - 4.344082995581108758e-1716j 2.2e-145, 3.34e-380j
0.01800978855065073355 + 9.2919069834850062778e-1714j 7.91e-146, 1.2e-380j
0.016476698634070814464 - 9.6102592297335361708e-1714j 6.78e-146, 1.03e-380j
0.0064194403104300537328 - 1.8797453157412524689e-1713j 1.35e-146, 2.05e-381j
0.016476698634070814464 - 4.0246607214310909242e-1715j 6.93e-146, 1.05e-380j
0.0081662145214355963802 + 1.3940496632806936479e-1715j 9.28e-147, 1.41e-381j
0.0009644786972996856751 + 1.4634225509135268014e-1716j 1.15e-146, 1.75e-381j
0.019492355390678281515 - 9.0363312642959675266e-1714j 1.28e-147, 1.94e-382j
0.0026939324381584941423 - 4.8330061563386287037e-1713j 2.04e-147, 3.1e-382j
0.019492355390678281515 - 5.5844715679727678472e-1715j 6.99e-148, 1.06e-382j
0.020901604687196324164 + 6.4608714714938187148e-1715j 1.85e-148, 2.82e-383j
0.0081662145214355963802 + 1.5131802838114216884e-1713j 5.16e-148, 7.84e-383j
0.020901604687196324164 + 8.8123538123368071803e-1714j 1.07e-148, 1.63e-383j
0.025010303786222474717 - 7.9282272846129340347e-1714j 2.91e-150, 4.41e-385j
0.0064194403104300537328 - 1.035559346632192734e-1715j 5.64e-148, 8.56e-383j
0.025010303786222474717 - 9.080568690074829283e-1715j 1.06e-151, 1.61e-386j
0.01163432987879694488 + 2.2440593124513293866e-1715j 1.73e-148, 2.63e-383j
0.014922316674705628567 + 1.0027257200377487962e-1713j 5.18e-151, 7.87e-386j
0.030248544095378816885 - 6.1606097085906873745e-1714j 2.48e-154, 3.76e-389j
0.004592186312957240445 + 7.2202127037682967297e-1716j 5.44e-148, 8.26e-383j
0.022275983783383036963 - 7.362337830303687276e-1715j 4.37e-151, 6.63e-386j
0.026328827256117806232 + 9.8493169058320467024e-1715j 5.33e-153, 8.09e-388j
0.004592186312957240445 + 2.6465517058053754988e-1713j 3.12e-151, 4.73e-386j
0.026328827256117806232 + 7.5348548375047668728e-1714j 2.08e-154, 3.16e-389j
0.022275983783383036963 - 8.5706310347851571416e-1714j 2.64e-153, 4e-388j
0.0098988185584637342564 - 1.7958023145397738257e-1715j 3.5e-150, 5.32e-385j
0.031486442671908101723 + 1.1985589943742286412e-1714j 9.7e-158, 1.47e-392j
0.023652796111646742441 + 8.244569773983336722e-1715j 1.08e-153, 1.63e-388j
0.023652796111646742441 + 8.2762306396411160491e-1714j 8.33e-154, 1.26e-388j
0.02763851250625891748 - 7.0983423150349669604e-1714j 8.1e-156, 1.23e-390j
0.0098988185584637342564 - 1.2980341575708775125e-1713j 7.93e-154, 1.2e-388j
0.030248544095378816885 - 1.1565854188529969987e-1714j 2.96e-158, 4.49e-393j
0.02895664662280256532 + 1.1087991150549720325e-1714j 6.72e-158, 1.02e-392j
0.01163432987879694488 + 1.1566596242226192606e-1713j 2.65e-154, 4.02e-389j
0.031486442671908101723 + 5.7093421514579739022e-1714j 1.79e-160, 2.72e-395j
0.013319182623224480414 - 1.0633034862958734586e-1713j 2.02e-154, 3.07e-389j
0.02763851250625891748 - 1.0522538142374204697e-1714j 7.6e-158, 1.15e-392j
0.034924401536824426727 - 1.3122824087034496572e-1714j 4.27e-163, 6.49e-398j
0.01800978855065073355 + 4.7692746636259890674e-1715j 8.59e-156, 1.3e-390j
0.033837039973617684395 + 4.9026791354095621745e-1714j 6.95e-163, 1.06e-397j
0.034924401536824426727 - 4.5620538207182713787e-1714j 5.56e-164, 8.44e-399j
0.032681549859728225887 - 5.2876941489611776853e-1714j 3.85e-162, 5.84e-397j
0.033837039973617684395 + 1.2734764920125056566e-1714j 7.7e-164, 1.17e-398j
0.032681549859728225887 - 1.2367365701218941265e-1714j 5.74e-163, 8.72e-398j
0.02895664662280256532 + 6.6312156501568635036e-1714j 1.61e-161, 2.45e-396j
0.035923327979178295404 + 4.2685796240114773669e-1714j 5.1e-166, 7.74e-401j
0.040885984686796626865 + 3.103727132138226272e-1714j 3.87e-171, 5.88e-406j
0.035923327979178295404 + 1.3562201608178209181e-1714j 5.29e-167, 8.03e-402j
0.036843126793975669448 - 1.4068900797837129579e-1714j 3.25e-168, 4.93e-403j
0.04131548575089313764 + 2.2972095658636546347e-1714j 4.57e-173, 6.94e-408j
0.037690495873735108557 + 3.807064117858186308e-1714j 8.25e-170, 1.25e-404j
0.036843126793975669448 - 4.0185089756433690874e-1714j 9.75e-169, 1.48e-403j
0.041526726218663177939 - 2.6658302864618809798e-1714j 3e-174, 4.55e-409j
0.038448938380160261685 - 1.5341524631938129453e-1714j 6.34e-172, 9.63e-407j
0.037690495873735108557 + 1.4655771803479668045e-1714j 6.59e-171, 1e-405j
0.0405708077402920748 - 3.1812627094862276106e-1714j 3.21e-174, 4.87e-409j
0.038448938380160261685 - 3.6312630287765576853e-1714j 2.47e-172, 3.74e-407j
0.041509874077500830777 + 2.7707770000730425596e-1714j 1.96e-175, 2.97e-410j
0.041127659157477998931 - 2.1677640616360470623e-1714j 7.38e-176, 1.12e-410j
0.03910585431065133485 + 1.6140419078269242706e-1714j 1.71e-174, 2.6e-409j
0.041509874077500830777 + 2.5497811834929585928e-1714j 7.5e-176, 1.14e-410j
0.039673331321470100669 - 3.3681924108872177896e-1714j 1.87e-175, 2.83e-410j
0.040164336203738224447 + 3.2678027404358657833e-1714j 1.34e-175, 2.04e-410j
0.041445019132841936 - 2.425578753659771989e-1714j 1.44e-176, 2.18e-411j
0.039673331321470100669 - 1.7052240977795050529e-1714j 4.77e-177, 7.25e-412j
0.040885984686796626865 + 2.0404244701727393765e-1714j 1.55e-177, 2.35e-412j
0.041127659157477998931 - 3.0286842142746635205e-1714j 5.46e-178, 8.28e-413j
0.03910585431065133485 + 3.4871566906971219314e-1714j 3.72e-177, 5.64e-412j
0.04131548575089313764 + 2.9501611422097650728e-1714j 1.92e-178, 2.92e-413j
0.0405708077402920748 - 1.9191564373925683337e-1714j 4.74e-179, 7.28e-414j
0.040164336203738224447 + 1.8070508967763336664e-1714j 4.56e-179, 7.04e-414j
0.041445019132841936 - 2.8648628197774756085e-1714j 4.79e-179, 7.08e-414j

Download

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