Rule: Q[2, 14, 31]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{16}-\frac{935281}{4314}\cdot t^{14}+\frac{38001691}{8628}\cdot t^{12}-\frac{245286041}{5752}\cdot t^{10}+\frac{2383796415}{11504}\cdot t^8-\frac{11245499265}{23008}\cdot t^6+\frac{22854346515}{46016}\cdot t^4-\frac{15081381315}{92032}\cdot t^2+\frac{1321665345}{184064}$
• $P_3$:
  $4\cdot t^{47}-\frac{1732125991151833729636853908176152627054278575186609793780268990181976454747178650212465373000768373163}{1073680216591424305473978241064322678500045691591461397310006456321533714374686191619620217432165722}\cdot t^{45}+\frac{13981127972967022109745464846606073441213823118237353482756684884332319269570437866494648752830883273993151}{47241929530022669440855042606830197854002010430024301481640284078147483432486192431263289567015291768}\cdot t^{43}-\frac{2065389527889724425033412350927540655964996273183407523691369691126129759380477764513543623822412293510478457}{62989239373363559254473390142440263805336013906699068642187045437529977909981589908351052756020389024}\cdot t^{41}+\frac{309563480198497495670036301900653258605493021127910292130039635850844425937041031808836967299470755303897101195}{125978478746727118508946780284880527610672027813398137284374090875059955819963179816702105512040778048}\cdot t^{39}-\frac{632855880918823320916021307863158433972723086287285243765251263330622106517784406459934804887283044440987732577025}{4787182192375630503339977650825460049205537056909129216806215453252278321158600833034680009457549565824}\cdot t^{37}+\frac{78258166055709033366837692757520155643255032439341198710841672098056159198280110527558055522705526838249363751433115}{14796744958251948828505385466187785606635296357719126670128302310052496629035675302107192756505153203456}\cdot t^{35}-\frac{2379924573500361689875291515828268328421102521877587261406467590429560080725024996647009816581074206657136803643784595}{14796744958251948828505385466187785606635296357719126670128302310052496629035675302107192756505153203456}\cdot t^{33}+\frac{111537356546861793676692305170899470578138847903836339801671985067991397811316205131136131677560365762478624699016939835}{29593489916503897657010770932375571213270592715438253340256604620104993258071350604214385513010306406912}\cdot t^{31}-\frac{4059136033556172424365999895226519884339485753632223610592364202469296347708985486281668648201659739490757807698135100575}{59186979833007795314021541864751142426541185430876506680513209240209986516142701208428771026020612813824}\cdot t^{29}+\frac{3110358782714704171129427596981887147800252885149470172870462502902409750119077682465374346263162609939107089892371652175}{3199296207189610557514677938635196887921145158425757117865578877849188460332037903158311947352465557504}\cdot t^{27}-\frac{1270241635076104772320121356824965251551305289934462078623924544537539040224924777962541833234093509082054520766564164948375}{118373959666015590628043083729502284853082370861753013361026418480419973032285402416857542052041225627648}\cdot t^{25}+\frac{21744838766906101287160553662834009038783519950863989246108157818106636955310900929068411523839338517314627082998320529390375}{236747919332031181256086167459004569706164741723506026722052836960839946064570804833715084104082451255296}\cdot t^{23}-\frac{12456117266728613466786008306496118136390208626138053399971052170993282310064940300170597740224645250633514640983867898521625}{20586775594089667935311840648609093017927368845522263193221985822681734440397461289888268182963691413504}\cdot t^{21}+\frac{62440578638815486160810954369181222767308026391311496394252307408342855362126522381228109439616324322237481898828045337024375}{20586775594089667935311840648609093017927368845522263193221985822681734440397461289888268182963691413504}\cdot t^{19}-\frac{98723289823771858925219327042456464612605020716347718037473205181376826183360754757264299067013876104371018412755703339801875}{8668116039616702288552353957309091797022050040219900291882941399023888185430510016795060287563659542528}\cdot t^{17}+\frac{31986749098583582937513896323822477477511444146707005046294608540100006361331117930806544094537565760528771449504570015700625}{1019778357601964975123806347918716682002594122378811799045051929296928021815354119622948269125136416768}\cdot t^{15}-\frac{125618380358749398311133798480569597885981731667585242312295080247019615446902556814763445356058031070342828352359949751894375}{2039556715203929950247612695837433364005188244757623598090103858593856043630708239245896538250272833536}\cdot t^{13}+\frac{5289813726115922816113988788617725232866161123545875741059975790532684350032645433003070083446126049071967147535506259654375}{63736147350122810945237896744919792625162132648675737440315745581058001363459632476434266820321026048}\cdot t^{11}-\frac{1187360231992559729377559653342786101109280446030105280154449132884703766869209560971844013150083534775006871628525897720384375}{16316453721631439601980901566699466912041505958060988784720830868750848349045665913967172306002182668288}\cdot t^9+\frac{1253331878592363327058401995792140857623932843882077829393440665185005797372719269503470039791673433937630400764481276585528125}{32632907443262879203961803133398933824083011916121977569441661737501696698091331827934344612004365336576}\cdot t^7-\frac{704466284715521764115660713634314446981219727024655387590185056679462707361507885103437102164119507545717907475908258301578125}{65265814886525758407923606266797867648166023832243955138883323475003393396182663655868689224008730673152}\cdot t^5+\frac{170162263710157537339166355161491188915640234291350639283447249397195981995596705844562445364810537797659323134085761390515625}{130531629773051516815847212533595735296332047664487910277766646950006786792365327311737378448017461346304}\cdot t^3-\frac{76279256453084276840471975895347039104748116150525158051544198923118499467928905948703945410074344146192737981695260921875}{1763940942879074551565502872075618044545027671141728517267116850675767389086017936645099708756992720896}\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.