Rule: Q[1, 2, 80]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-3\cdot t$
• $P_3$:
  $t^{83}-\frac{8841120095951272791998597635676341309389209747}{2536715008713235491535654685913474885538809}\cdot t^{81}+\frac{4886891469315758811402735682602128894976520332180}{845571669571078497178551561971158295179603}\cdot t^{79}-\frac{394966668858608594894972062713183645147746524677420}{65043974582390653629119350920858330398431}\cdot t^{77}+\frac{295430108865590646258597136755334547203802520386881530}{65043974582390653629119350920858330398431}\cdot t^{75}-\frac{167577865200915553470094826347966268180025794174587833150}{65043974582390653629119350920858330398431}\cdot t^{73}+\frac{74982104751865594640800689906964175845930241016091910711700}{65043974582390653629119350920858330398431}\cdot t^{71}-\frac{27180612113734212785903445285099289811298260385218594428813500}{65043974582390653629119350920858330398431}\cdot t^{69}+\frac{8135510717143087900845115837808611653105669387751727382745978875}{65043974582390653629119350920858330398431}\cdot t^{67}-\frac{2039108736278358797979707385608829430462822442408527045530549323625}{65043974582390653629119350920858330398431}\cdot t^{65}+\frac{432555483993408325676907313255703399081038571220350983985565992754000}{65043974582390653629119350920858330398431}\cdot t^{63}-\frac{78293346653846626885771937505928759113655188667429950264001718114262000}{65043974582390653629119350920858330398431}\cdot t^{61}+\frac{12167736076108058913145213905196518565409976156022027154349516430585755000}{65043974582390653629119350920858330398431}\cdot t^{59}-\frac{1631469664878477835695820366154173864400359551145119121128748994015796585000}{65043974582390653629119350920858330398431}\cdot t^{57}+\frac{189408499546971306289060385555136123217322170804416353112393956954719017090000}{65043974582390653629119350920858330398431}\cdot t^{55}-\frac{19090116272481817791570927687500946163407331925050623515194942330572085125510000}{65043974582390653629119350920858330398431}\cdot t^{53}+\frac{1673304632610185642937705049284364214049817599997464417723640791711249303528348750}{65043974582390653629119350920858330398431}\cdot t^{51}-\frac{127685475093965604643227296361203207983213405346245791390083788140148333171661156250}{65043974582390653629119350920858330398431}\cdot t^{49}+\frac{8485042712488262689653611983037167860962445391921874428125108437594260613808148875000}{65043974582390653629119350920858330398431}\cdot t^{47}-\frac{490885952845435357117629836458820699150019251594107092004457204039549229861066218625000}{65043974582390653629119350920858330398431}\cdot t^{45}+\frac{24701372856756484965591672209090231655000854765761678965717026887207474371268337631937500}{65043974582390653629119350920858330398431}\cdot t^{43}-\frac{1079467315049548549416008703079160064189257532837447445720177153501662260169797590003312500}{65043974582390653629119350920858330398431}\cdot t^{41}+\frac{40879817716001180052522359588968224414320555218757136847723098349990480015797566486514375000}{65043974582390653629119350920858330398431}\cdot t^{39}-\frac{1337825389015999574775264434533124013047096285078395005562588649392113810100180723495063125000}{65043974582390653629119350920858330398431}\cdot t^{37}+\frac{37701419014748704003287865262759845481697757003394474299353316102294197202088664490038026718750}{65043974582390653629119350920858330398431}\cdot t^{35}-\frac{911020766926421391396178990719966890511858491881550995225406172978182220938756070893495630906250}{65043974582390653629119350920858330398431}\cdot t^{33}+\frac{18779492998744725974132630160089989004589072069979289581639823353734254830423054515996827972250000}{65043974582390653629119350920858330398431}\cdot t^{31}-\frac{328225529934291302049767993546167611356826589352337352900725363395571200733256506653892098388750000}{65043974582390653629119350920858330398431}\cdot t^{29}+\frac{4828883644241250912014040003416388475146422260409066196928201873191816184444903690218107423536875000}{65043974582390653629119350920858330398431}\cdot t^{27}-\frac{59288706332992502015571099284313263846628258630980810781219171654444666736152186204073364709425625000}{65043974582390653629119350920858330398431}\cdot t^{25}+\frac{601312692477546912684895074927936878733808547308036134547901068437056272398850208472310154305256250000}{65043974582390653629119350920858330398431}\cdot t^{23}-\frac{4976251463586055087714904087878177519591536471015639767895272140109853773914618528731720173019768750000}{65043974582390653629119350920858330398431}\cdot t^{21}+\frac{33107914016691905011189088602069138042292899933616602771639576107025701999815949262049554591208794921875}{65043974582390653629119350920858330398431}\cdot t^{19}-\frac{173897557709565312729745435478540996218107407385727724117144221935553440970371020224540013288872306640625}{65043974582390653629119350920858330398431}\cdot t^{17}+\frac{704943698421453925242407829167258563050060969552677662761351652538803886312237577092020247511377976562500}{65043974582390653629119350920858330398431}\cdot t^{15}-\frac{2142891498013939798697501749261059423683076928687333287162379252006182026228973219857641325601800179687500}{65043974582390653629119350920858330398431}\cdot t^{13}+\frac{4703729118320955280280190023877410176134603722219372769754857683857896852629339701618314135450510597656250}{65043974582390653629119350920858330398431}\cdot t^{11}-\frac{7082404491044430310433385878546996523943416453393435710437409487215278261178596175089521538702927324218750}{65043974582390653629119350920858330398431}\cdot t^9+\frac{6795264516263777305860429397704072966599392647116468455540996201922379459156250072001581359112793320312500}{65043974582390653629119350920858330398431}\cdot t^7-\frac{3705090669856544713539544935596606668415254943341731618051787021547481276222912555024862055252769960937500}{65043974582390653629119350920858330398431}\cdot t^5+\frac{937798188508148488673176202722755050242324615328264286164605560514958787840422613973756613899662802734375}{65043974582390653629119350920858330398431}\cdot t^3-\frac{69462710455036156021570695479001836588841621572275292767043734071442482192081738233509588828253642578125}{65043974582390653629119350920858330398431}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.