Rule: Q[1, 10, 68]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{11}-55\cdot t^9+990\cdot t^7-6930\cdot t^5+17325\cdot t^3-10395\cdot t$
• $P_3$:
  $t^{79}-\frac{767007228865468331878975927722704541678144958491485534901120009987575447430170984684271046848894645730150673947}{278992975266353450884842938790475369805965211710115148809543320841659739728192887469054532243203545009412347}\cdot t^{77}+\frac{60951275612997744900430107180017621341179695440884949511706225481565601335250653755659230254558228236985053007941361}{17018571491247560503975419266218997558163877914317024077382142571341244123419766135612326466835416245574153167}\cdot t^{75}-\frac{16698853828869187292789414628271573378080518273991464265753781115485565131254632223747553561287246802299978583893397655}{5672857163749186834658473088739665852721292638105674692460714190447081374473255378537442155611805415191384389}\cdot t^{73}+\frac{573907061202252308947337056338803044181660605207934300609615676748450981139958736800344854034536809579776316745668310788325}{334698572661202023244849912235640285310556265648234806855182137236377801093922067333709087181096519496291678951}\cdot t^{71}-\frac{7317590993664360745547910032727478206681846769434859604931926260114514767728517207085830973826593420452359666465929180992416185}{9706258607174858674100647454833568274006131703798809398800281979854956231723739952677563528251799065392458689579}\cdot t^{69}+\frac{841805465176329462662942227316917165325086497696834781483639401456269409734052684365686240224623818045233191947006066656639066845}{3235419535724952891366882484944522758002043901266269799600093993284985410574579984225854509417266355130819563193}\cdot t^{67}-\frac{234147061632293467395620459406486979982479563768637405431592566553537214327358654462149320293816597182223481412880961499013059687785}{3235419535724952891366882484944522758002043901266269799600093993284985410574579984225854509417266355130819563193}\cdot t^{65}+\frac{53484738674492972411142668786857793930540384949036367062647092427367678136752271971251441825283729194890394507557261617312678557071300}{3235419535724952891366882484944522758002043901266269799600093993284985410574579984225854509417266355130819563193}\cdot t^{63}-\frac{5379379673572807277583135909560193614347449591631349094828575620385581905678187488002238493777324212789456045042103714148949949910700}{1710956920002619191627119241112915260709700635254505446642038071541504712096552080500187471928750055595356723}\cdot t^{61}+\frac{14588746826210624278731617316570421653951264857295937046613664735064738049312913142734653816083723421863885289165545705441218803978300}{28999269830552867654696936290049411198469502292449244858339628331211944272822916618647245286927967043989097}\cdot t^{59}-\frac{68250313882417029226257598292425257143154330358235420809402503909833943646742188527872182429718540598176769395079433485860583373676700}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{57}+\frac{7897945865151071177229981228703790034231483084883769090110992838490792129632610351138431882929616087654187959850559367303688550246437100}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{55}-\frac{783028300366838584459735542757904799746918815538414409566705877677197988207147980871907381360307919295088653807941275839841074813636511500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{53}+\frac{66725975040860524851009484284931465280724787167907574191896872998534555960779399997688740803719197772138739073634687861529911502195069976500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{51}-\frac{4898033143959101772073018959456019529321159374426354020465863055420282264928205547190796155393911220839703626026061410907882965118110747422500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{49}+\frac{310116890531114959685970020953408615516858848669749579745318825625823059325489050336371664084333222472749330991539017338555642492985289453503750}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{47}-\frac{16944347153839044397445238955509961694157696374640561389707555088377256178972242180076848491376629592220362478947340252166603251153999982417023750}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{45}+\frac{798756266795375136796841254884497576793447944747071649670238142768153423459773893296273767622042482283396538275500350823059299647909544086221656250}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{43}-\frac{32454575943799105716501428761881849796933004824262245197282969462868266217662023211317254207933189234078628815961698552418833367487492203058156581250}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{41}+\frac{1134702469555573629886363223228780735288971761038712782546397276633747625129617465460342715827300758315003197550505966727503304057021690850486932681250}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{39}-\frac{34055479308148258479204167615306376659428988087942256685382789668370818303376732124196303615602053897466003075084170308330182169124485931726804509931250}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{37}+\frac{874602025773262567795122248217747772361958435709514411790805320426710723761345224566207571380000939545744029214304707349757237042635826771050382306168750}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{35}-\frac{19142966187245358326550958715172761600273216082647908526891719313600878834676208777179078023262954586659852745374235918171299291977904615343928352838093750}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{33}+\frac{355334717636094603286404028553587543305112403278496183762859012960055934556114892177957116202899062937681221102486978294176160899313398295117216306862562500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{31}-\frac{5560244112234275082200410831202078608734428265771366444276028019580317298424167313831893781955479192471649154213887382690874677430964787451587583694019562500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{29}+\frac{72819587075437863845278249183072793242713225837598024613713608765134776176841082675609410665887240541490177207667363641240617313595564552102577686534066437500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{27}-\frac{791313332655738811902234690274948164573420702356417559346112600157351056873611641726287151089870045013806937871376299789450062848237997206569683369025956187500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{25}+\frac{7061449442420570264058890199736830589838645500284699619567497137567261467074379248754048575492706504930499208398241669003569556821624806879814198932563450937500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{23}-\frac{51105163619372427953016023517027864761877298410928686761676031329485797954418820952535052746580802731428616239146392633444413661051266904937675045370427623437500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{21}+\frac{295453030636685748477787050119319955550029323406272203449420073046988117239573832292643480219973587255587626918945518794201278185217021113238175001218726631562500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{19}-\frac{1339387002193468170255239904239224481563667957341418913596099426397561363814420919968869183088576389280732035359978894417407252331094069990699360903043491400312500}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{17}+\frac{4652475995042156536152165008441969646767326077357959230171230813683344466725010670443688749174885658141513386075820061743296892627568391008593120736379766116953125}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{15}-\frac{12024427988336459304461665874220261622252854447021158297984604281123301550610329719096404978506860152454477620065049738727641321475415726488472672351429709389453125}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{13}+\frac{22251099583030657202796931682857941248876990334412251881764974422959317198716535529360123116217335720388995137932408672867570328910869710925613346942769416923046875}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^{11}-\frac{27978188565113255538760103615768411858781139670206800837177822243323884182028029544602114692407789558105325252176203900319473236837802846908225562461249971758984375}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^9+\frac{22170785691500288945288891805635186466906173965026489807262712764713575270189757501875206416171978875262095427428809445095002428940610151062992780222676020493359375}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^7-\frac{9846354293389470395352349664690723772985713290295177619536956609806829779017106290667848555690566760541606371830595042822881689862459779951189881378391804890234375}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^5+\frac{1990457206597768341041996440407600868081049999653228658741512222952262500710793901233338962244501197480590960758973687911596348809374629254018752473351941478515625}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\cdot t^3-\frac{114028584017848871078593389642007626559134231758494939132735551682396974820464790178812215195181037053107385024421044744926472822916172113032960308075062689453125}{999974821743202332920584010001703834429982837670663615804814770041791181821479883401629147825102311861693}\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.