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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{16}-\frac{935281}{8628}\cdot t^{14}+\frac{38001691}{8628}\cdot t^{12}-\frac{245286041}{2876}\cdot t^{10}+\frac{2383796415}{2876}\cdot t^8-\frac{11245499265}{2876}\cdot t^6+\frac{22854346515}{2876}\cdot t^4-\frac{15081381315}{2876}\cdot t^2+\frac{1321665345}{2876}$
• $P_3$:
  $t^{47}-\frac{1732125991151833729636853908176152627054278575186609793780268990181976454747178650212465373000768373163}{2147360433182848610947956482128645357000091383182922794620012912643067428749372383239240434864331444}\cdot t^{45}+\frac{13981127972967022109745464846606073441213823118237353482756684884332319269570437866494648752830883273993151}{47241929530022669440855042606830197854002010430024301481640284078147483432486192431263289567015291768}\cdot t^{43}-\frac{2065389527889724425033412350927540655964996273183407523691369691126129759380477764513543623822412293510478457}{31494619686681779627236695071220131902668006953349534321093522718764988954990794954175526378010194512}\cdot t^{41}+\frac{309563480198497495670036301900653258605493021127910292130039635850844425937041031808836967299470755303897101195}{31494619686681779627236695071220131902668006953349534321093522718764988954990794954175526378010194512}\cdot t^{39}-\frac{632855880918823320916021307863158433972723086287285243765251263330622106517784406459934804887283044440987732577025}{598397774046953812917497206353182506150692132113641152100776931656534790144825104129335001182193695728}\cdot t^{37}+\frac{78258166055709033366837692757520155643255032439341198710841672098056159198280110527558055522705526838249363751433115}{924796559890746801781586591636736600414706022357445416883018894378281039314729706381699547281572075216}\cdot t^{35}-\frac{2379924573500361689875291515828268328421102521877587261406467590429560080725024996647009816581074206657136803643784595}{462398279945373400890793295818368300207353011178722708441509447189140519657364853190849773640786037608}\cdot t^{33}+\frac{111537356546861793676692305170899470578138847903836339801671985067991397811316205131136131677560365762478624699016939835}{462398279945373400890793295818368300207353011178722708441509447189140519657364853190849773640786037608}\cdot t^{31}-\frac{4059136033556172424365999895226519884339485753632223610592364202469296347708985486281668648201659739490757807698135100575}{462398279945373400890793295818368300207353011178722708441509447189140519657364853190849773640786037608}\cdot t^{29}+\frac{3110358782714704171129427596981887147800252885149470172870462502902409750119077682465374346263162609939107089892371652175}{12497250809334416240291710697793737843441973275100613741662417491598392423172023059212156044345568584}\cdot t^{27}-\frac{1270241635076104772320121356824965251551305289934462078623924544537539040224924777962541833234093509082054520766564164948375}{231199139972686700445396647909184150103676505589361354220754723594570259828682426595424886820393018804}\cdot t^{25}+\frac{21744838766906101287160553662834009038783519950863989246108157818106636955310900929068411523839338517314627082998320529390375}{231199139972686700445396647909184150103676505589361354220754723594570259828682426595424886820393018804}\cdot t^{23}-\frac{12456117266728613466786008306496118136390208626138053399971052170993282310064940300170597740224645250633514640983867898521625}{10052136520551595671538984691703658700159848069102667574815422764981315644725322895453255948712739948}\cdot t^{21}+\frac{62440578638815486160810954369181222767308026391311496394252307408342855362126522381228109439616324322237481898828045337024375}{5026068260275797835769492345851829350079924034551333787407711382490657822362661447726627974356369974}\cdot t^{19}-\frac{98723289823771858925219327042456464612605020716347718037473205181376826183360754757264299067013876104371018412755703339801875}{1058119633742273228583051020179332494753668217800280797348991869998033225760560304784553257759235784}\cdot t^{17}+\frac{31986749098583582937513896323822477477511444146707005046294608540100006361331117930806544094537565760528771449504570015700625}{62242331396604307563708883539960734985509895164722399844058345294001954456503547340267838691719752}\cdot t^{15}-\frac{125618380358749398311133798480569597885981731667585242312295080247019615446902556814763445356058031070342828352359949751894375}{62242331396604307563708883539960734985509895164722399844058345294001954456503547340267838691719752}\cdot t^{13}+\frac{42318509808927382528911910308941801862929288988367005928479806324261474800261163464024560667569008392575737180284050077235000}{7780291424575538445463610442495091873188736895590299980507293161750244307062943417533479836464969}\cdot t^{11}-\frac{1187360231992559729377559653342786101109280446030105280154449132884703766869209560971844013150083534775006871628525897720384375}{124484662793208615127417767079921469971019790329444799688116690588003908913007094680535677383439504}\cdot t^9+\frac{1253331878592363327058401995792140857623932843882077829393440665185005797372719269503470039791673433937630400764481276585528125}{124484662793208615127417767079921469971019790329444799688116690588003908913007094680535677383439504}\cdot t^7-\frac{704466284715521764115660713634314446981219727024655387590185056679462707361507885103437102164119507545717907475908258301578125}{124484662793208615127417767079921469971019790329444799688116690588003908913007094680535677383439504}\cdot t^5+\frac{170162263710157537339166355161491188915640234291350639283447249397195981995596705844562445364810537797659323134085761390515625}{124484662793208615127417767079921469971019790329444799688116690588003908913007094680535677383439504}\cdot t^3-\frac{76279256453084276840471975895347039104748116150525158051544198923118499467928905948703945410074344146192737981695260921875}{841112586440598750860930858648118040344728313036789187081869531000026411574372261354970793131348}\cdot t$

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.