Rule: Q[1, 4, 14, 32]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_3$:
  $t^{19}-\frac{10067}{33}\cdot t^{17}+\frac{4654486}{165}\cdot t^{15}-\frac{13098722}{11}\cdot t^{13}+26061308\cdot t^{11}-305527040\cdot t^9+1871898210\cdot t^7-5508762714\cdot t^5+6473363715\cdot t^3-1927283085\cdot t$
• $P_4$:
  $t^{51}-\frac{91214001897741174196706706436901730314473441311201869922067362781851886351747401051114582450993520784466907}{87745432851566710976812014670979861123532323561578632873722248162267583652943548832103083537299186737097}\cdot t^{49}+\frac{104244869410590565928623772137048990764693172557328977996224563884137905585523817468233756930664445281948932997082}{211905220336533607009001015430416364613330561401212398390039229311876214521858670429528946742577535970089255}\cdot t^{47}-\frac{29865733193241724452774161908185364331324527636415223835624398801750484052021528463845160305313928992982903575858754}{211905220336533607009001015430416364613330561401212398390039229311876214521858670429528946742577535970089255}\cdot t^{45}+\frac{4260431270272415622835699581694101328099434908412301347943488162047535156076760101135552757137632433352226222255266632}{155397161580124645139934077982305334049775745027555758819362101495375890649363024981654560944556859711398787}\cdot t^{43}-\frac{256336294163073537077173873966725087663864481579610285851855486522028677456190817836016188833564844780473417882855885004}{66598783534339133631400319135273714592761033583238182351155186355161095992584153563566240404810082733456623}\cdot t^{41}+\frac{39381343406078301533049087994299714734679625441592776891599800815389658498895305312886464542545787480856388034049216379570}{97336683627111041461277389505400044404804587544732728051688349288312371066084532131366043668568582456590449}\cdot t^{39}-\frac{1057870773026573844514376972320229943899883824722001971312624744298090243894308536768072312656892597616687639705360272904222}{32445561209037013820425796501800014801601529181577576017229449762770790355361510710455347889522860818863483}\cdot t^{37}+\frac{199124845866541242925118575943555937344495760290113276778839932383968942131331371385061965978746259042105424864376260954280217}{97336683627111041461277389505400044404804587544732728051688349288312371066084532131366043668568582456590449}\cdot t^{35}-\frac{3530125776103452256869600338891658870547845088648255544017543166182018409755303697972009194368607859312351232466751352718865}{34975452255519598081666327526194769818470926174894979537078098917826938938585890093915215116266109398703}\cdot t^{33}+\frac{11616481322521507178668262564049108221936923369776021772711922816124634552279658721150611619701508560369329219104397148439421820}{2949596473548819438220526954709092254691048107416143274293586342070071850487410064586849808138441892623953}\cdot t^{31}-\frac{359351834705616911286435601122654365572835878376731922455585290538858958834237900990206546992954323602589670597621513186091393900}{2949596473548819438220526954709092254691048107416143274293586342070071850487410064586849808138441892623953}\cdot t^{29}+\frac{8808826464918053147508944930147158613198291776261014995663473364137447024346035173567650021402552051370076066670337605535887495800}{2949596473548819438220526954709092254691048107416143274293586342070071850487410064586849808138441892623953}\cdot t^{27}-\frac{18951293373119823416902783301613412836344743527623395034828017298679946191870138405989847035621876597725191284192324678796957487200}{327732941505424382024502994967676917187894234157349252699287371341119094498601118287427756459826876958217}\cdot t^{25}+\frac{12527553674752203132188034949514183399217963982961115919368777260419513099470918605188560665647320397645575622926484245987049477500}{14249258326322799218456651955116387703821488441623880552142929188744308456460918186409902454775081606879}\cdot t^{23}-\frac{148242219662961870328951772304219188574570832329489392359741202080212770039850273660165252178604065114761335154569489059394723587500}{14249258326322799218456651955116387703821488441623880552142929188744308456460918186409902454775081606879}\cdot t^{21}+\frac{70989539468764148941305034038429465822977650016253173774664313699953004517516543743214350635505001985167949227962500662933883939375}{749960964543305222024034313427178300201130970611783186954891009933910971392679904547889602882899031941}\cdot t^{19}-\frac{488697517246311774721733036523319972126698854315125143720403800550834581700766303942402006366459125198945303393596079145670993067125}{749960964543305222024034313427178300201130970611783186954891009933910971392679904547889602882899031941}\cdot t^{17}+\frac{2492248854063568461340362032759211008796880586407720214494909993861001074616721055808853368233602222959313725241561298731566497911750}{749960964543305222024034313427178300201130970611783186954891009933910971392679904547889602882899031941}\cdot t^{15}-\frac{9158696627360625365983352865963340280001967243717623529675931212809796901536162525481485652280930785035630966766053715076911945238750}{749960964543305222024034313427178300201130970611783186954891009933910971392679904547889602882899031941}\cdot t^{13}+\frac{2125434282988656787304059934763635460455242804309170812024733264774140431704134182894009474239276538173214753977186101055349051410000}{68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631}\cdot t^{11}-\frac{3587534274037109392472540316095752102709076589421897833340317407238884510095043056122632732664491220431478008681584272946650211812500}{68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631}\cdot t^9+\frac{3746007474731968033415951257432775161674963049642010608059030380596976623721070289206273094359505484382665291986772145786496186713750}{68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631}\cdot t^7-\frac{2219310648906916213752359931061841966738562452272968828659954339608998834883307913580768811551632749025955833327504948139057224708750}{68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631}\cdot t^5+\frac{670507374594183255728158314758949414630309045933833808293058810642897214501074999360767931853605591411520612283255919151341897028125}{68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631}\cdot t^3-\frac{79678458941391570434768471026367654053172733616464304519083624029612598960238255597343453992703801589737820348969847674287371771875}{68178269503936838365821301220652572745557360964707562450444637266719179217516354958899054807536275631}\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.