Rule: Q[4, 69]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{73}-\frac{1404934439395278923134934088544538317874454497229579263821570244907}{564032284581165233520782981146660289488340845610857060255025647}\cdot t^{71}+\frac{107400317000518977095221122054998770130639056799579682818880050091804708}{36662098497775740178850893774532918816742154964705708916576667055}\cdot t^{69}-\frac{79384950227133590830952701449688352357129669252198250670193818439274703593}{36662098497775740178850893774532918816742154964705708916576667055}\cdot t^{67}+\frac{3764937673682516660333826348404315493355468771391642827444500330861108888609}{3332918045252340016259172161321174437885650451336882628779697005}\cdot t^{65}-\frac{22706437958406749617155973781661641816944868677593123968070936775969132815336}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{63}+\frac{6953562278674460875787320800719519602398546111035989179180545563262299475802912}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{61}-\frac{1707381720937419558488620475378879880561995500517496392451504647380615879152803352}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{59}+\frac{342364671414220930354570689596927004196681557746151785567406715349280411011965738212}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{57}-\frac{56815825527340086280804489878973358242554070013540270673063505023288331570498522326636}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{55}+\frac{7880244938765356171188168667202643957454753972556217252450709525630009193754096828773520}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{53}-\frac{920142688511261480761218570355539092933317256959086501875294398340884556149795605086663940}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{51}+\frac{90932313906580179317374550222532532833415579900633555131367196150755675854490867925342960100}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{49}-\frac{7633986889788148529362714273181927096891684283396062785989817151909742027632974934946504636600}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{47}+\frac{545775007782847529886605949700845685953122510582819250817436748854227157089175255941707963880800}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{45}-\frac{33272032638965162273957052719475417815422227187369108280849277977326581824494455983330411317029000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{43}+\frac{1730178145289650727659385584669821218432064199212696791487700647655303322895585897763191855688281750}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{41}-\frac{76699283251495518673602539642051766572203897308161553538313810927112813031615121928941652787465377750}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{39}+\frac{2894291003523011739967550406260596214176990986155043343940330675972997354982250201324801727222183309000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{37}-\frac{92752856913798583996130841959091188745004366443340457409717742956734509000584882545947278503809399163250}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{35}+\frac{2516198111664493967750209473812546276201558983976695781026428540043262695096377761775556366657066575798750}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{33}-\frac{57542300218665793090149939491841967242848565959718536153086600436898471438510418560784519505357243549535000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{31}+\frac{1103588909751343343909235943369208631678061142889298069162455166242672046370620818862635783717762299284620000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{29}-\frac{17638782117492762485223200438858239461036854036912460746970868823688950169932584884084840049388157310584945000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{27}+\frac{233170874844825859076077486044132793076275163254122869263093971278601800710367135990837118604425793863590872500}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{25}-\frac{2526203169836942229728113104481492371595084427335367289410021311239567835888312919695963092332190585976168687500}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{23}+\frac{22186779308054620053321616834517513466583952613421588664252819880782757982287203814437866780151184272010146250000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{21}-\frac{155880833036597762378330623972064252176374116836410265795977329312154163032090987795542469956533119675862770862500}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{19}+\frac{861983750333773847735991910238356478877869073079343758751011201857295459529688854197329375612930912271217125612500}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{17}-\frac{3676050548961329342573170766388588059969473221836759400871743495816942053054619285451237790971017560790623028525000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{15}+\frac{11778971666189152602770385325232510120683693701221896301307172225326658306242220349922673073760389083971714886500000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{13}-\frac{27392611591514362364500960609412856523250400344757275690181573809205982631232182897064911860892392823470210354875000}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^{11}+\frac{44066272116326541910790033708396174983536592998575203791879709761921263794385431639145722923990131508674758214953125}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^9-\frac{45703598946711829066686598069231368092718638906050157399519466712654447243897603747190888643433406797659030072140625}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^7+\frac{27334003330756925288184560273748056904634176749446256803518246010613362937481530200268340238266922812527073501187500}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^5-\frac{7716469243966586089876510817176331439722498843870811620499746716610251911396765669184502745822497803715590296796875}{51275662234651384865525725558787299044394622328259732750456877}\cdot t^3+\frac{648800250868216572192932614330187149618583666558413767471608743496526824136819987508757309150915358403041926015625}{51275662234651384865525725558787299044394622328259732750456877}\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.