Rule: Q[1, 6, 52]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^7-21\cdot t^5+\frac{105}{2}\cdot t^3-\frac{105}{4}\cdot t$
• $P_3$:
  $2\cdot t^{59}-\frac{20272901550173121694599172315995340688525092889295501}{12967689434123817553800621450329162601323511747202}\cdot t^{57}+\frac{1386441581282803288210920173345825568700053819801933350031}{2437925613615277700114516832661882569048820208473976}\cdot t^{55}-\frac{14358746797147277253976121174840684640809757855200353737035085}{112144578226302774205267774302446598176245729589802896}\cdot t^{53}+\frac{4489444398019304394930556259635980025064482471760750279118470865}{224289156452605548410535548604893196352491459179605792}\cdot t^{51}-\frac{1036587417113168210440398154408511156175115310787887202195297821775}{448578312905211096821071097209786392704982918359211584}\cdot t^{49}+\frac{1952449500926438180539811105975005476761897837020823318397530560425}{9544219423515129719597257387442263674574104645940672}\cdot t^{47}-\frac{11813818004274626362865625851920137542189744083105689360998912875275}{829932123783924323443239772821066406484704751820928}\cdot t^{45}+\frac{1314352230208759963968195444517126495311678836699488973289278226257625}{1659864247567848646886479545642132812969409503641856}\cdot t^{43}-\frac{14784953566066101938962534595578672734689548187549525000697068220390375}{414966061891962161721619886410533203242352375910464}\cdot t^{41}+\frac{17358309318677714433323643684138482118262660889025483272805424940916250875}{13278913980542789175091836365137062503755276029134848}\cdot t^{39}-\frac{1044064285007874497479070558744669852837501688913252573269628491370335936375}{26557827961085578350183672730274125007510552058269696}\cdot t^{37}+\frac{51631467335266124834148335342072674849652867610142225350597440802861979459875}{53115655922171156700367345460548250015021104116539392}\cdot t^{35}-\frac{2101669122359628449486915378345107762905043457242014673753255531888526767985625}{106231311844342313400734690921096500030042208233078784}\cdot t^{33}+\frac{17594494748944385388769618761960227237089104035156152118516127102888743818873125}{53115655922171156700367345460548250015021104116539392}\cdot t^{31}-\frac{483651741902964191914987117512546870364320956333017993696696885920309362375255625}{106231311844342313400734690921096500030042208233078784}\cdot t^{29}+\frac{84941326355000753070985507877637956601600783708569260369013251196668545502805625}{1659864247567848646886479545642132812969409503641856}\cdot t^{27}-\frac{397559309802084048045656510020645243362040444142801390513581307381855427623080100625}{849850494754738507205877527368772000240337665864630272}\cdot t^{25}+\frac{11735048167526070710044831836570652508948371022984752496090322515092860268068882234375}{3399401979018954028823510109475088000961350663458521088}\cdot t^{23}-\frac{138457854513909035849500329280770038659124567835498765277632083170939251530470717921875}{6798803958037908057647020218950176001922701326917042176}\cdot t^{21}+\frac{1289666344318983137566252485776345322054048440447693621791577465219097361944389123859375}{13597607916075816115294040437900352003845402653834084352}\cdot t^{19}-\frac{9331429397250466051575768815568053769219549829852975762419611176178807364975567331265625}{27195215832151632230588080875800704007690805307668168704}\cdot t^{17}+\frac{25680937712182869372464922610627378368421584915993396098325013717912014383439342678234375}{27195215832151632230588080875800704007690805307668168704}\cdot t^{15}-\frac{104612386703708333417852096718135840410086285171652560733755299335962258892108492787421875}{54390431664303264461176161751601408015381610615336337408}\cdot t^{13}+\frac{303946270857136099779407660528349249292950955455271302805835781701690530990305508703203125}{108780863328606528922352323503202816030763221230672674816}\cdot t^{11}-\frac{299216462919582266625826907007426147677330215822427570401741670047718681013846243450328125}{108780863328606528922352323503202816030763221230672674816}\cdot t^9+\frac{1482357832525645851011123525324247162415517435559008157421258894549627970418401706114328125}{870246906628852231378818588025622528246105769845381398528}\cdot t^7-\frac{1028105291115911582992110397850422517300481573434051739988141526067482164946389697672390625}{1740493813257704462757637176051245056492211539690762797056}\cdot t^5+\frac{325086924193912032931006284789417207958603668942397228378506493334152661444907508373203125}{3480987626515408925515274352102490112984423079381525594112}\cdot t^3-\frac{29378913991473419250019369200245955176799956107233952385493240330212054366035412887734375}{6961975253030817851030548704204980225968846158763051188224}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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