Rule: Q[5, 14, 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.

• $P_1$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_2$:
  $t^{19}-\frac{10067}{33}\cdot t^{17}+\frac{4654486}{165}\cdot t^{15}-\frac{13098722}{11}\cdot t^{13}+26061308\cdot t^{11}-305527040\cdot t^9+1871898210\cdot t^7-5508762714\cdot t^5+6473363715\cdot t^3-1927283085\cdot t$
• $P_3$:
  $t^{53}-\frac{418313987895796250264732305810739641229306913167703306430698070705020000777059650337582482009037701865687390802718891}{365647758348046586595500362053237969559139497873017676422564541071752736738173161518266278197126512852408009787982}\cdot t^{51}+\frac{16462827807300024611693792015458431408196782819802555465548554989184822593357585388047232296287467361923027342877637513949}{27423581876103493994662527153992847716935462340476325731692340580381455255362987113869970864784488463930600734098650}\cdot t^{49}-\frac{23710489848670123246244362811111077002587731742727486155419535769349673532697287270803940475807278854495788487699119647754247}{123406118442465722975981372192967814726209580532143465792615532611716548649133442012414868891530198087687703303443925}\cdot t^{47}+\frac{54273887334014933163555752018813161981736077900906860808992473875832794843796756881526158763105992998400220411653169317035984853}{1290154874625778012930714345653754426683100160108772596922798750031582099513667802857064538411452070916735079990550125}\cdot t^{45}-\frac{6337324987196839790549676660688430191049955204757099148246041376403938157939667642853526901805168010909079040241543818629576417928}{946113574725570542815857186812753246234273450746433237743385750023160206310023055428513994835064852005605725326403425}\cdot t^{43}+\frac{25128289810794307376935429662546928856562270786960177357316736302975561765534252860474189530680779679315188643302724126790171709215176}{31221747965943827912923287164820857125731023874632296845531729750764286808230760829140961829557140116184988935771313025}\cdot t^{41}-\frac{93336941376442000523112262838937597054902382383410385210592399869353138004978664663323931759466100129235184818887679756201971517158161}{1248869918637753116516931486592834285029240954985291873821269190030571472329230433165638473182285604647399557430852521}\cdot t^{39}+\frac{3780429536935091471912084794679350662460681590702911031411675119279586733580363480135712689857274621134089399886544695281698073430361396}{693816621465418398064961936996019047238467197214051041011816216683650817960683573980910262879047558137444198572695845}\cdot t^{37}-\frac{19675612583885186083146855202824090171091647337670888378128343488486281947418485898516603375736732432898573800221087929188251444272017010797}{62443495931887655825846574329641714251462047749264593691063459501528573616461521658281923659114280232369977871542626050}\cdot t^{35}+\frac{1501065663988698894945515035526991613253772712131281254939770275011319649024028970165661388262454584910409935217283710902255988448727586133}{103212389970062241034457147652300354134648012808701807753823900002526567961093424228565163072916165673338806399244010}\cdot t^{33}-\frac{101684363950728325139513121651230784204358988596737557177128569378769876730268106199691111228356293162253131924316406348842656960682688257222}{189222714945114108563171437362550649246854690149286647548677150004632041262004611085702798967012970401121145065280685}\cdot t^{31}+\frac{601730183386478933035629519183261152951300531199524809439654084403969328081261112652223192780449659507264431082195666825050529052527588726594}{37844542989022821712634287472510129849370938029857329509735430000926408252400922217140559793402594080224229013056137}\cdot t^{29}-\frac{14225346010251876965559858740649907233101297000491252616002929161428677630483452910616554677627444754804899444975819145177908601376909713917348}{37844542989022821712634287472510129849370938029857329509735430000926408252400922217140559793402594080224229013056137}\cdot t^{27}+\frac{29717682302381490560743630364619496663146065275506930044067811115314968611736297301449882002093588257236575257955934222450578818000210360805844}{4204949221002535745848254163612236649930104225539703278859492222325156472488991357460062199266954897802692112561793}\cdot t^{25}-\frac{19183232425702920412769802520718448978208371912172246223196396308909389932887797960228454694514990086240061205601351278645305249938973745830350}{182823879174023293297750181026618984779569748936508838211282270535876368369086580759133139098563256426204004893991}\cdot t^{23}+\frac{20245279301030738131040344357715279603947975249740307275145339994889106990640528318965903289141957984874080192025417994395480201495617879226525}{16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181}\cdot t^{21}-\frac{3990700336751610178349853028161271515584063384962194934400052274915505837893705066779359633459358062918955239717274094346609972030875138749395025}{365647758348046586595500362053237969559139497873017676422564541071752736738173161518266278197126512852408009787982}\cdot t^{19}+\frac{27135560299877185261490284835057347844610551043411824292449073654870838868656336850490179640345778403073825981635738038691349092062199720944271925}{365647758348046586595500362053237969559139497873017676422564541071752736738173161518266278197126512852408009787982}\cdot t^{17}-\frac{68506612845678183544803107619820902745731888836270474373747324414924817225584755890940899333019988767707143286465920010328647769368226650610258865}{182823879174023293297750181026618984779569748936508838211282270535876368369086580759133139098563256426204004893991}\cdot t^{15}+\frac{249676922209743617518631686833453433035074261154824953873003060030490099093112806822655335027954728651072866623311211147729787249383297616516681075}{182823879174023293297750181026618984779569748936508838211282270535876368369086580759133139098563256426204004893991}\cdot t^{13}-\frac{57505511035068646366861992977632215176011798374521515540472931115934514329476426692148292911652071864043840225590259902079817176385051024392619300}{16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181}\cdot t^{11}+\frac{96195595793638055662088044207360958881829203396126558218658143487636891915698131594811228722679118464562188381033704780749953137515449816359260500}{16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181}\cdot t^9-\frac{98724767160899566735103082734342816657805176155820245672356273754525872350836173889783921616874767688785562093876933531237230665303793540356319625}{16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181}\cdot t^7+\frac{55623616037735957027352135700475755519563293971078623688630482045993697015772636420165581622219605435024247028913985729566308338824944094098261450}{16620352652183935754340925547874453161779068085137167110116570048716033488098780069012103554414841493291273172181}\cdot t^5-\frac{28599230390192992312300186415823301038870396008838771089465037831926841345196879265270546102731887793373731462880112003127270458629143582999630875}{33240705304367871508681851095748906323558136170274334220233140097432066976197560138024207108829682986582546344362}\cdot t^3+\frac{2261401261503784852686748288065936459450081809965977621022129425940392794138749914464118549708448634974341368003205127494969342536214366421290375}{33240705304367871508681851095748906323558136170274334220233140097432066976197560138024207108829682986582546344362}\cdot t$

Warning: This rule has negative weights!

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.