Rule: Q[1, 4, 64]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^5-10\cdot t^3+\frac{15}{2}\cdot t$
• $P_3$:
  $2\cdot t^{69}-\frac{183641803813822461634886460508999049042744525556260410142}{81336797374064149466377530038708517437375496175393683}\cdot t^{67}+\frac{2928075043991523606281566918233788134170635685217130159064643}{2440103921221924483991325901161255523121264885261810490}\cdot t^{65}-\frac{97507381113890810960409699541454327127290301336599420801637992}{244010392122192448399132590116125552312126488526181049}\cdot t^{63}+\frac{41608267510680424001583611578128543649798380376520538926851241}{444463373628765844078565737916439985996587410794501}\cdot t^{61}-\frac{7299049148035046644479685132172549180284929280909966446362814415}{444463373628765844078565737916439985996587410794501}\cdot t^{59}+\frac{3985986503670432399429096403290663054161972988848725728620823482795}{1777853494515063376314262951665759943986349643178004}\cdot t^{57}-\frac{217283025703591858613954371146499869424616168335661836574794893947667}{888926747257531688157131475832879971993174821589002}\cdot t^{55}+\frac{308182307998855405853743402971311536561340326511828931362523411151902135}{14222827956120507010514103613326079551890797145424032}\cdot t^{53}-\frac{22503112985575670655919379167036681267782383287021804477363594978133614095}{14222827956120507010514103613326079551890797145424032}\cdot t^{51}+\frac{5465148864176195521818330352134609633300686712202546612143383751363399584625}{56891311824482028042056414453304318207563188581696128}\cdot t^{49}-\frac{69448111348953232441624503492543727555833167493216712759124741474244538367625}{14222827956120507010514103613326079551890797145424032}\cdot t^{47}+\frac{23755342398423672583271537864851670339650641970007785188187186000319246928175275}{113782623648964056084112828906608636415126377163392256}\cdot t^{45}-\frac{857084805983517261506996257843220057913564455101408862157857530613981269032773625}{113782623648964056084112828906608636415126377163392256}\cdot t^{43}+\frac{104556845343582622346260135467051182792075010869331298710491434811669316984187109625}{455130494595856224336451315626434545660505508653569024}\cdot t^{41}-\frac{1348396118776092620727110194230775295120850003195558238019789148990987526399996396875}{227565247297928112168225657813217272830252754326784512}\cdot t^{39}+\frac{940624073751035477013931078460530845564914725431315590566919391609724444073445319284375}{7282087913533699589383221050022952730568088138457104384}\cdot t^{37}-\frac{17301011513456969370869365917959313282209055215875979053986073398098495115644604312658875}{7282087913533699589383221050022952730568088138457104384}\cdot t^{35}+\frac{1070956930576470695409933307408982285273260968331183150434022289311762074773315999050145625}{29128351654134798357532884200091810922272352553828417536}\cdot t^{33}-\frac{1736167661223433443338618007287175078695326329904532670921402971144808894112791284169991875}{3641043956766849794691610525011476365284044069228552192}\cdot t^{31}+\frac{150179633860563515315857794381008950528779863022309536456148331286970141670668325586703084375}{29128351654134798357532884200091810922272352553828417536}\cdot t^{29}-\frac{1344979897500539638040175451969552454788154239446094602907285123461007966937707861440588215625}{29128351654134798357532884200091810922272352553828417536}\cdot t^{27}+\frac{39584664393889583278931439591009948760609792409790384095528650634195056258915515352585951033125}{116513406616539193430131536800367243689089410215313670144}\cdot t^{25}-\frac{118455412238887356763380904717634271744766841093194065855766459678068722741319147407336133890625}{58256703308269596715065768400183621844544705107656835072}\cdot t^{23}+\frac{9114069772046830379819470822011085814688985509640511923209204483710810349826830612313793864109375}{932107252932313547441052294402937949512715281722509361152}\cdot t^{21}-\frac{34686845457690826176122595731997994927596282309150329484434127923335675601939759912355200258859375}{932107252932313547441052294402937949512715281722509361152}\cdot t^{19}+\frac{410139083731590022608282083886807846109183971555651450410260748241622432061459537057225684453765625}{3728429011729254189764209177611751798050861126890037444608}\cdot t^{17}-\frac{229901871089319261386591770063992134907935882634477932944396888000581234807426588465170832307096875}{932107252932313547441052294402937949512715281722509361152}\cdot t^{15}+\frac{3034150320022061066016175130484969544538030083137109383747737472374067383346641309833368580300453125}{7456858023458508379528418355223503596101722253780074889216}\cdot t^{13}-\frac{3537437914550396528200270162163544710266832479075792292489015681462416525534286206099107136896609375}{7456858023458508379528418355223503596101722253780074889216}\cdot t^{11}+\frac{11032128308231107270661599915151101977442314600355620063515446603423541822470972761547982448960234375}{29827432093834033518113673420894014384406889015120299556864}\cdot t^9-\frac{2655309982802181482122218566102260054484650724860189782958808449329766545665142758995638520970390625}{14913716046917016759056836710447007192203444507560149778432}\cdot t^7+\frac{44582197433195077618140417099560501593988561137091552541941372408172274275427180430563136411744203125}{954477827002689072579637549468608460301020448483849585819648}\cdot t^5-\frac{5109463417058460694317733698069262148431137730033117948613949855650228975453166293531076919308515625}{954477827002689072579637549468608460301020448483849585819648}\cdot t^3+\frac{619847406337382353412739727573191093613596493728477625638156881103818404990886343827120928006796875}{3817911308010756290318550197874433841204081793935398343278592}\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.