Rule: Q[1, 6, 85]

Type

This rule is of Laguerre 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)
430.8956791873722732 - 1.8623314102460415046e-6043j 1.11e-2020, 1.11e-2020j
326.13846578173984577 - 2.083717517564569774e-6036j 1.91e-2013, 1.91e-2013j
268.1172347824327907 - 3.2059258173427792822e-6029j 3.6e-2007, 3.6e-2007j
247.56023695410465746 - 2.8390925981079855075e-6027j 3.5e-2005, 3.5e-2005j
95.230018946105701361 + 9.5848607908337717946e-6020j 1.4e-1998, 1.4e-1998j
71.022761043239685429 - 4.4956554471883934046e-6028j 3.42e-2000, 3.42e-2000j
292.67533656315494458 - 1.2796068342653966824e-6036j 1.02e-2009, 1.02e-2009j
191.60323296857171616 + 1.0579365982776866572e-6024j 1.03e-2000, 1.03e-2000j
111.29373697548437158 - 6.2980567364880348639e-6026j 3.55e-1998, 3.55e-1998j
307.57421725898324441 - 5.3390997656343330018e-6058j 2.34e-2011, 2.34e-2011j
103.04089593035126959 - 5.4859757800387014951e-6043j 2.53e-1998, 2.53e-1998j
64.920824544685131639 + 1.6785612153924481167e-6062j 6.99e-2001, 6.99e-2001j
17.545208844207002095 - 9.0482246728955541597e-6096j 2.63e-2013, 2.63e-2013j
184.92422859560149037 + 3.0861536773691171766e-6080j 2.36e-2000, 2.36e-2000j
32.867821015627437616 + 2.2659236101402236355e-6125j 3.56e-2007, 3.56e-2007j
39.170529985306072485 + 2.5630848467183245992e-6119j 1.99e-2005, 1.99e-2005j
20.498598446324716138 + 1.2120416679321038021e-6138j 7.22e-2012, 7.22e-2012j
10.596691202183363172 - 6.666280368484227212e-6144j 1.89e-2017, 1.89e-2017j
9.8078186402891763344 + 4.1627217032139497355e-6144j 3.15e-2018, 3.15e-2018j
166.28161157077034751 - 1.8261727755143513081e-6123j 2.67e-1999, 2.67e-1999j
12.448513062956781353 - 9.2382410861715449246e-6164j 3.39e-2016, 3.39e-2016j
257.45899102883484735 - 6.9618281261985953443e-6146j 4.05e-2006, 4.05e-2006j
4.779596384709730006 + 8.3811582004940727822e-6181j 1.65e-2024, 1.65e-2024j
229.53119282556934172 + 2.1133656552825289064e-6154j 1.34e-2003, 1.34e-2003j
67.929289191405053799 - 7.8721202888039103587e-6192j 1.56e-2000, 1.56e-2000j
178.48898448547844882 - 2.1383963931796944696e-6256j 6.07e-2000, 6.07e-2000j
43.722366839867042043 - 6.8148908039799862634e-6312j 2.36e-2004, 2.36e-2004j
124.5700895638531643 + 1.1507413161473086084e-6349j 3.92e-1998, 3.92e-1998j
51.095584288829616489 - 3.108032765567016749e-6392j 6.72e-2003, 6.72e-2003j
59.151998646122438214 - 9.4733740606334279163e-6452j 1.27e-2001, 1.27e-2001j
154.86606813557939561 + 1.2247288160666595326e-6550j 7.74e-1999, 7.74e-1999j
279.74200802812161254 - 2.1388058975492201146e-6678j 2.41e-2008, 2.41e-2008j
7.9886543552868417152 + 4.7180771852777032248e-6757j 2.57e-2020, 2.57e-2020j
172.27986414344134721 - 4.4385764140114510815e-6840j 1.28e-1999, 1.28e-1999j
7.1061439463269785179 + 1.0353850423066262868e-6952j 2.13e-2021, 2.13e-2021j
149.42670846603113215 - 1.5905495723339115255e-6960j 1.24e-1998, 1.24e-1998j
25.408506447588580981 + 2.1561809117116014957e-7033j 9.18e-2010, 9.18e-2010j
8.9059997307057955863 - 2.2985916476684698409e-7044j 2.84e-2019, 2.84e-2019j
1 - 7.9787659601183622605e-7057j 4.03e-2033, 4.03e-2033j
238.283427701367059 - 4.5617159370589519083e-7022j 2.15e-2004, 2.15e-2004j
30.903357369320565818 + 4.5633824068120181239e-7065j 8.56e-2008, 8.56e-2008j
18.989963815544515587 + 1.3665470502476051911e-7080j 1.36e-2012, 1.36e-2012j
53.703415905778286223 - 7.3106719303989662642e-7066j 1.89e-2002, 1.89e-2002j
29.005783347094213687 - 9.0173557652586268063e-7104j 2.03e-2008, 2.03e-2008j
23.707564614046122743 + 3.7337584823777012639e-7118j 1.81e-2010, 1.81e-2010j
115.59526693367579109 - 5.758087873282004062e-7120j 4.23e-1998, 4.23e-1998j
37.000555077078835665 + 6.7664977319194345172e-7172j 5.01e-2006, 5.01e-2006j
80.832457201813052796 - 5.3433424717259962596e-7177j 2.2e-1999, 2.2e-1999j
61.99561227384457231 - 1.1240950935824488758e-7233j 3.08e-2001, 3.08e-2001j
6.2736817166099937228 - 2.6305052926049344625e-7332j 1.87e-2022, 1.87e-2022j
198.54658909635100995 + 1.5797683477414780658e-7306j 3.33e-2001, 3.33e-2001j
27.174384358136486448 + 1.690990246412585863e-7373j 4.32e-2009, 4.32e-2009j
14.850773039696224542 + 4.822255978570904963e-7391j 8.18e-2015, 8.18e-2015j
139.03848651336788319 + 1.3619047286359239371e-7373j 2.42e-1998, 2.42e-1998j
1.3014961014684251586 - 2.486638052253594391e-7450j 5.69e-2032, 5.69e-2032j
3.527641360716346235 - 8.5835527529096358644e-7445j 1.64e-2026, 1.64e-2026j
107.11026930552612614 - 4.4552205732333049891e-7415j 2.88e-1998, 2.88e-1998j
48.563615374592630243 + 8.9104080522489640845e-7442j 2.09e-2003, 2.09e-2003j
74.203103939712486548 + 6.4207429579655043415e-7437j 6.42e-2000, 6.42e-2000j
13.607410327915846949 - 1.211343980212268728e-7512j 1.6e-2015, 1.6e-2015j
16.164909452595574328 + 1.5697167152471029427e-7510j 4.7e-2014, 4.7e-2014j
221.23133655318230071 - 5.3906645254001304545e-7496j 6.34e-2003, 6.34e-2003j
87.834801721477073801 - 3.3214700410783652721e-7626j 5.91e-1999, 5.91e-1999j
120.01915985305794522 + 1.5242788965526734974e-7789j 4.03e-1998, 4.03e-1998j
2.9900188560786498298 + 2.5569595815336427567e-7890j 1.49e-2027, 1.49e-2027j
0.18796958875044643007 - 4.3177581140997883307e-7907j 2.32e-2038, 2.32e-2038j
160.48091471386691825 - 9.7026043011621693054e-7911j 4.68e-1999, 4.68e-1999j
144.15360417361145678 + 4.6914754095947862641e-7979j 1.84e-1998, 1.84e-1998j
134.07391212877973522 - 1.2347264785396815004e-8002j 2.87e-1998, 2.87e-1998j
91.481951562916153298 - 4.0855158316477343676e-8009j 9.34e-1999, 9.34e-1999j
0.53237458389455870629 + 1.0926846051568245569e-8050j 1.63e-2035, 1.63e-2035j
11.419627275641631169 + 1.4711210332653496177e-8032j 6.98e-2017, 6.98e-2017j
205.77861408361961195 + 1.9273133250414898431e-8015j 9.67e-2002, 9.67e-2002j
99.081946665752325214 + 1.1515743599497354927e-8012j 1.79e-1998, 1.79e-1998j
129.25315029470578819 + 3.7887770169000851879e-8018j 3.57e-1998, 3.57e-1998j
0.077296120870346398912 - 2.0871251770557625038e-8063j 5.53e-2040, 5.53e-2040j
46.106267490255812041 + 1.0540221549752156652e-8027j 6.94e-2004, 6.94e-2004j
213.3284072778101675 + 4.5791116566921210481e-8027j 2.62e-2002, 2.62e-2002j
0.74914715176924397419 + 6.2729028574590867233e-8058j 2.87e-2034, 2.87e-2034j
56.388423911950285434 + 1.5429438218053098273e-8025j 4.83e-2002, 4.83e-2002j
4.1230307266186984333 + 2.3052520056889663546e-8050j 1.56e-2025, 1.56e-2025j
2.5026000900489822054 - 1.2068335446732018886e-8052j 1.27e-2028, 1.27e-2028j
2.0583222307489643231 + 7.2814909826770536394e-8054j 1.11e-2029, 1.11e-2029j
34.899945169068445327 - 2.277673793650410871e-8030j 1.42e-2006, 1.42e-2006j
84.2858249147951929 - 2.7373085620922128297e-8022j 3.98e-1999, 3.98e-1999j
1.6562944335710357542 + 7.9382824575565036489e-8055j 7.83e-2031, 7.83e-2031j
77.472299547533516922 + 1.2607039222279543298e-8023j 1.24e-1999, 1.24e-1999j
41.410803848771036589 + 4.14437416414919887e-8030j 6.37e-2005, 6.37e-2005j
5.4971242933953402093 - 8.8722153981645469869e-8048j 1.99e-2023, 1.99e-2023j
0.014745104103879904395 - 2.3818913251481385485e-8065j 1.19e-2041, 1.19e-2041j
22.071058071845552848 + 1.2093537085763201881e-8035j 3.78e-2011, 3.78e-2011j
0.34247063828229575625 - 5.9796804888291209e-8061j 6.59e-2037, 6.59e-2037j

Weights

Weight (ball center) Error (ball radius)
3.8857569629928362158e-175 - 1.7841617843103477676e-6130j 1.12e-388, 3.62e-1893j
4.9929263094723975667e-141 + 8.7939618204755642037e-6114j 7.3e-378, 2.36e-1882j
4.012775565589264212e-116 + 4.4174147639508389037e-6101j 1.02e-370, 3.31e-1875j
2.9296482856209811294e-107 + 1.566293822880919976e-6096j 5.52e-368, 1.79e-1872j
1.6666849743714755162e-41 - 8.4096316016660557353e-6061j 9.87e-334, 3.2e-1838j
4.4839850786169112646e-31 + 2.3109297184756747735e-6056j 4.51e-323, 1.46e-1827j
1.0750393548465805852e-126 + 1.7352415349160477892e-6106j 2.05e-374, 6.63e-1879j
4.1759836116525203631e-83 - 5.0003942516215058639e-6084j 4.9e-360, 1.59e-1864j
1.9646965198561094757e-48 + 2.3164319552821249822e-6065j 7.39e-341, 2.39e-1845j
4.3020845975797797066e-133 - 9.5125751403619492414e-6110j 9.22e-377, 2.99e-1881j
7.1357337700145052608e-45 + 3.474138185795665074e-6063j 5.59e-338, 1.81e-1842j
1.8945082231992603605e-28 + 4.7949587754315475981e-6055j 3.54e-323, 1.15e-1827j
3.3904596159793929585e-08 + 1.4866975529570054788e-6043j 5.39e-281, 1.74e-1785j
3.1983925834300036708e-80 + 1.6071763310069193631e-6082j 4.01e-359, 1.3e-1863j
1.0624711530532044009e-14 - 1.1878807428504998785e-6047j 2.56e-302, 8.29e-1807j
2.1471208921893093732e-17 + 3.5316898397449865905e-6049j 5.02e-308, 1.62e-1812j
1.9285967780248305499e-09 + 2.0100625197433754803e-6044j 2.87e-287, 9.3e-1792j
1.8700893552127933525e-05 + 5.8762175842888293366e-6041j 2.57e-267, 8.32e-1772j
4.7194196470943626078e-05 - 8.1975546813613326988e-6041j 5.15e-265, 1.67e-1769j
3.5931406995414647801e-72 - 2.7288812261098915839e-6078j 3.02e-357, 9.77e-1862j
4.3408436866937414236e-06 + 9.5678253610900217075e-6042j 8.17e-274, 2.65e-1778j
1.5767117022974708961e-111 - 1.0031550666316161426e-6098j 5.7e-372, 1.85e-1876j
0.00577266870633023764 - 7.1263528365241556867e-6040j 2.63e-249, 8.51e-1754j
1.7623239821027811147e-99 + 1.5964478010131133712e-6092j 1.18e-368, 3.83e-1873j
9.6178797900416061792e-30 - 1.0653516119099834405e-6055j 1.34e-328, 4.35e-1833j
1.9226435215815935871e-77 - 4.5920015885873126491e-6081j 1.21e-359, 3.92e-1864j
2.4111963682068832268e-19 + 2.9715284440598908767e-6050j 3.5e-317, 1.13e-1821j
3.6658399786897582522e-54 - 1.3160666441165440491e-6068j 1.49e-349, 4.81e-1854j
1.6571048933648200235e-22 - 5.8808074341423995191e-6052j 2.43e-322, 7.88e-1827j
5.7317789782941876118e-26 + 8.9806630551113013875e-6054j 3.09e-326, 1e-1830j
3.0541538297273668037e-67 - 1.1160407139627128479e-6075j 7.62e-357, 2.47e-1861j
3.9457947519135011438e-121 - 1.2079984303454590011e-6103j 9.93e-378, 3.22e-1882j
0.0003067033359961382805 - 1.311817384350665042e-6040j 3.72e-278, 1.21e-1782j
9.2305877059074481388e-75 + 1.177082384549349132e-6079j 1.45e-359, 4.7e-1864j
0.00070431718635460421833 + 1.88790120135268041e-6040j 5.35e-277, 1.73e-1781j
6.8162669297712066056e-65 + 1.9936465656459729903e-6074j 3.17e-356, 1.03e-1860j
1.5999421682570070683e-11 - 9.2814854815635830857e-6046j 1.1e-309, 3.55e-1814j
0.0001252047304543511763 + 9.9336449882671866465e-6041j 4.43e-283, 1.43e-1787j
0.10090917842232860997 - 7.1030187643846948299e-6039j 9.65e-272, 3.13e-1776j
2.9451058297588929419e-103 - 1.7995250094104274945e-6094j 8.57e-372, 2.78e-1876j
7.3215168887032804657e-14 + 3.6500424099640077304e-6047j 1.77e-314, 5.72e-1819j
8.3573053482621460459e-09 - 5.4765181670066223354e-6044j 5.44e-303, 1.76e-1807j
1.2575480788373258304e-23 + 1.5018837090503708806e-6052j 1.75e-328, 5.68e-1833j
4.7149922408062677631e-13 - 1.0961835907637979483e-6046j 2.24e-313, 7.24e-1818j
8.4391841222483580416e-11 + 2.6257675465510808793e-6045j 5.79e-309, 1.87e-1813j
2.7371311974435262915e-50 - 1.9650339895983810636e-6066j 8.55e-351, 2.77e-1855j
1.8209152508773921402e-16 - 1.1695355718994399667e-6048j 5.06e-320, 1.64e-1824j
2.6742527164973283748e-35 - 2.1325875906943978168e-6058j 1.1e-341, 3.57e-1846j
3.4329291131228632895e-27 - 2.1038888043468559771e-6054j 8.68e-333, 2.81e-1837j
0.001517953147501949748 - 2.8659223816792442174e-6040j 2.53e-289, 8.19e-1794j
4.1932077731351546372e-86 + 1.3684432602028545578e-6085j 2.63e-368, 8.52e-1873j
2.839446426085591217e-12 + 3.2217981204340704293e-6046j 9.3e-315, 3.01e-1819j
4.5454633459418259053e-07 + 1.1210141380676613818e-6042j 2.21e-305, 7.17e-1810j
2.0828994256692966433e-60 + 5.1076594534591583118e-6072j 1.98e-357, 6.4e-1862j
0.089499190879836968128 + 6.3400321708116936304e-6039j 9.2e-274, 2.98e-1778j
0.016612144881086239201 - 1.7319478196446973001e-6039j 1.09e-287, 3.53e-1792j
1.2534519407095907825e-46 - 2.7498423893587065894e-6064j 3.55e-349, 1.15e-1853j
2.0233261066890464696e-21 + 2.2370790947170933717e-6051j 1.83e-329, 5.94e-1834j
1.9162589421860981671e-32 - 4.8700406571728917902e-6057j 1.14e-339, 3.71e-1844j
1.4835404139428727248e-06 - 3.1994774926624820238e-6042j 1.43e-307, 4.63e-1812j
1.2860165760373564824e-07 - 4.0518161002474683588e-6043j 5.19e-310, 1.68e-1814j
6.7386745773844444541e-96 - 1.1335324849504286766e-6090j 3.47e-374, 1.12e-1878j
2.5694830917222417718e-38 - 1.0406811667148473575e-6059j 1.24e-345, 4.02e-1850j
3.3748805753660560384e-52 + 1.6356877644462715751e-6067j 2.25e-353, 7.3e-1858j
0.025699317810833986218 + 2.5174575667335612978e-6039j 1.42e-299, 4.6e-1804j
0.11071114173682241944 - 1.9104938637584732518e-6039j 2.33e-292, 7.56e-1797j
1.1490833294952673793e-69 + 5.7632038103829272343e-6077j 3.04e-362, 9.85e-1867j
1.2891018713986420626e-62 - 3.3039486937551843897e-6073j 2.05e-359, 6.65e-1864j
2.8966151574393062092e-58 - 7.40638411956122358e-6071j 7.6e-358, 2.46e-1862j
6.8826959817458559051e-40 + 3.0310277635009043483e-6060j 4.69e-349, 1.52e-1853j
0.11981039465853417086 - 5.2702611817905153161e-6039j 1.44e-303, 4.65e-1808j
1.0235059718686679747e-05 - 2.8245053301641365377e-6041j 6.73e-318, 2.18e-1822j
3.1613233474461333537e-89 - 3.2535190975728636787e-6087j 7.14e-374, 2.31e-1878j
3.6380307875061955166e-43 - 5.5468841634707346902e-6062j 6.77e-351, 2.19e-1855j
3.4901944353694439762e-56 + 1.0131992740776334164e-6069j 3.35e-357, 1.09e-1861j
0.08058295492622315665 + 8.9386344388546900341e-6040j 7.73e-313, 2.5e-1817j
2.2919002433084161069e-20 - 8.2694297645579720361e-6051j 6.84e-339, 2.22e-1843j
1.7388366599473343043e-92 + 6.6220985891779075044e-6089j 9.93e-376, 3.22e-1880j
0.10910890557186089365 + 6.8104283109762350356e-6039j 1.64e-315, 5.33e-1820j
8.8314945750241380777e-25 - 3.7259917793528036729e-6053j 1.53e-341, 4.97e-1846j
0.01013482281022134967 + 1.1269348393106239177e-6039j 4.29e-322, 1.39e-1826j
0.038076777766740973998 - 3.4081761143785977265e-6039j 6.54e-321, 2.12e-1825j
0.054081145954510195507 + 4.3355214621463903368e-6039j 1.18e-320, 3.83e-1825j
1.439872395909852026e-15 + 3.7741532969049360935e-6048j 2.39e-336, 7.76e-1841j
8.6954802258356286252e-37 + 4.5445673691126536966e-6059j 4.3e-349, 1.39e-1853j
0.072433304164279293969 - 5.3106011099048083321e-6039j 5.6e-324, 1.81e-1828j
7.49206342449902942e-34 + 1.0208043355135157557e-6057j 1.38e-347, 4.48e-1852j
2.3585260891787518719e-18 - 1.0384845471123673788e-6049j 3.63e-339, 1.17e-1843j
0.0030634642808939394616 + 4.4875378657352911606e-6040j 1.41e-328, 4.55e-1833j
0.037244499317878604846 - 2.4348983995607022434e-6040j 6.06e-328, 1.94e-1832j
4.1685209636123520204e-10 - 7.3118067962800900399e-6045j 4.17e-334, 1.35e-1838j
0.12352332731833924767 + 3.3915454164224690495e-6039j 3.71e-327, 1.18e-1831j

Download

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