Rule: Q[1, 4, 12, 34]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_3$:
  $t^{17}-\frac{6536}{53}\cdot t^{15}+\frac{617205}{106}\cdot t^{13}-\frac{7144995}{53}\cdot t^{11}+\frac{172854825}{106}\cdot t^9-\frac{539111430}{53}\cdot t^7+\frac{3204996795}{106}\cdot t^5-\frac{1892565675}{53}\cdot t^3+\frac{1129052925}{106}\cdot t$
• $P_4$:
  $t^{51}-\frac{354696408756689972035341792798958782630145129488255160445782133908844667752745790678583782583677}{361947278787276079606380737395009697201726430023372024265004165160073849850080265365484966647}\cdot t^{49}+\frac{37321986895249883451351006435242722675118320856984416653385007057664987829927553050200084292749121219}{84695663236222602627893092550432269145203984625469053678010974647457280864918782095523482195398}\cdot t^{47}-\frac{10232320370317224721146809214888878221154063070175806037821070009173496514466781783958634302296345184035}{84695663236222602627893092550432269145203984625469053678010974647457280864918782095523482195398}\cdot t^{45}+\frac{638987315580134318602311874719572080010883069339617741700959063140321335276138979037371627195925535697055}{28231887745407534209297697516810756381734661541823017892670324882485760288306260698507827398466}\cdot t^{43}-\frac{65952669946675402033554793565451275740381048501295372894087538678844184814998134728852403033214868962107991165}{21428002798764318464856952415259364093736608110243670580536776585806692058824451870167440995435694}\cdot t^{41}+\frac{6750447333553301089186055254357449690277569309657451435503214077385371566169921146745701240042008937541585153665}{21428002798764318464856952415259364093736608110243670580536776585806692058824451870167440995435694}\cdot t^{39}-\frac{197766103829307963551215226102760017653352691632560366792156085202205360523719100280528162412794365583267091795}{7962840133320073751340376222690213338437981460514184533830091633521624696701765838040669266234}\cdot t^{37}+\frac{2523394053217598097456913507765128689886756900999495973929219978872271991570410389462236396335928403123884174705225}{1648307907597255266527457878096874161056662162326436198502828968138976312217265528474418538110438}\cdot t^{35}-\frac{11160111960381113571174483775056913412210396340051286482081352546180262016466279763889397906355527526057831920922075}{149846173417932296957041625281534014641514742029676018045711724376270573837933229861310776191858}\cdot t^{33}+\frac{71795152406092846133846978118838515346907084928227981984181473784335227708334157023030038078114629045363579615037375}{24974362236322049492840270880255669106919123671612669674285287396045095639655538310218462698643}\cdot t^{31}-\frac{2203020059703572222501315036983886923939524097340230658668252787438330865855475011845440955339781571895709501618923375}{24974362236322049492840270880255669106919123671612669674285287396045095639655538310218462698643}\cdot t^{29}+\frac{53688031276435117347878917711835536445617092199030614640048881178985073030049195506079560463260779771297010893020807625}{24974362236322049492840270880255669106919123671612669674285287396045095639655538310218462698643}\cdot t^{27}-\frac{38346731162749672770576812670817877254662578513519509323176161610448756524325710856679034235414118517636347003495150375}{924976379123038870105195217787247003959967543393061839788343977631299838505760678156239359209}\cdot t^{25}+\frac{25282469009710782895435774258476188029444273259276235159129492556476604920598775515212741206315654675281493244309015625}{40216364309697342178486748599445521911302936669263558251667129462230427761120029485053885183}\cdot t^{23}-\frac{298703427390338629770826801652916819794278231946966846478700781601851111593028188879845578051073428610462413630276520625}{40216364309697342178486748599445521911302936669263558251667129462230427761120029485053885183}\cdot t^{21}+\frac{905145227368793648768775990423296971120116837940027995343590928694375414546091058315548544072712496903928745167833072500}{13405454769899114059495582866481840637100978889754519417222376487410142587040009828351295061}\cdot t^{19}-\frac{6228266507541905087432976809193712778491097291595901054167036255461010928387880964522420749051674655479536653510763473750}{13405454769899114059495582866481840637100978889754519417222376487410142587040009828351295061}\cdot t^{17}+\frac{63504972849781442462809123110125771853169606491706965755185662594051782620480169757264963832047554590030736312583244515625}{26810909539798228118991165732963681274201957779509038834444752974820285174080019656702590122}\cdot t^{15}-\frac{77749119371633040371441984733476231509086055001312426492522199306165984131948835035316114265440878636430042650500552571875}{8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374}\cdot t^{13}+\frac{198202775119120067346020611038100050418432821581832124086762158018332215746161766728135670042876189141606308455467398278125}{8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374}\cdot t^{11}-\frac{333260299449137705786273694957357432298545064688873198121098046259414702081963354388716386352714774068669298295467902340625}{8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374}\cdot t^9+\frac{343799035553830506326843076746090901585877881045553832538321708972669868247874505092234407935562655509649599231626142428125}{8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374}\cdot t^7-\frac{195441984601232991153874180297031047863381298236607370328457942037008319939633541146253022889590943324773095040543785703125}{8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374}\cdot t^5+\frac{51560998543633382826717179703722561934567634865412661772416994527114867396403421548903382124570800130780467216865153453125}{8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374}\cdot t^3-\frac{4414983813377993531404338743133537642138401133764684337047409149473624080545938214303116635706852445978240064237895078125}{8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374}\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.