Rule: Q[4, 7, 50]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{11}-41\cdot t^9+528\cdot t^7-2520\cdot t^5+4095\cdot t^3-1575\cdot t$
• $P_3$:
  $t^{61}-\frac{159780808144946850849720776913993034898630070509315114892399548236809303183552022919486788037287}{100371175104610794176270587397583032050826432384911432142286510164079626087515255181457820082}\cdot t^{59}+\frac{16920872504903924219997027400238389018654191869090700529397517223501415952918326013961477470525003}{14338739300658684882324369628226147435832347483558776020326644309154232298216465025922545726}\cdot t^{57}-\frac{2093600716791832125925342625322359603721497240126883928791982580491329339905329298486982427488820675590}{3864290241527515575786417614806946733956817646819090137478030641317065604369337324486126073157}\cdot t^{55}+\frac{667871905674191422322863550857891194654301058903291637280162276441507526401459045441546735476009828546315}{3864290241527515575786417614806946733956817646819090137478030641317065604369337324486126073157}\cdot t^{53}-\frac{28627075379380359541565710940045635397828854479955867115186947807498032407436045623173727424543101022138825}{702598225732275559233894111783081224355785026694380024996005571148557382612606786270204740574}\cdot t^{51}+\frac{56967521442231230933736363665681892900373349583112222123144510072101301641687628101512295517078974701931602025}{7728580483055031151572835229613893467913635293638180274956061282634131208738674648972252146314}\cdot t^{49}-\frac{82724225890473480051623940317632977237508693303252070045991350323989372021090702176347223237066714206217822400}{78863066153622766852784032955243810897077911159573268111796543700348277640190557642574001493}\cdot t^{47}+\frac{409518761565027971451951619385282387877725576972404418737068891675014947187814427063182369196226432138228499375}{3428828963200989863164523171967122212916430919981446439643327986971664245225676419242347891}\cdot t^{45}-\frac{6863287206773352659221944723911884862094451688670495298600320503945434678636242815098472382151148357211492532875}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{43}+\frac{516327969467520883350800159317927691247669367382949087029806823853024947118871288352265915658183810319906464637625}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{41}-\frac{15936118585274951401972355308513498079650972602666867566836438748918575478646648021221558943375494233174855851834750}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^{39}+\frac{809714338457269421062330249411447523797033880381290110396192980476660439859102028350988344474412997607166841796694875}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^{37}-\frac{67818338497390518085729472641532272570863036777524860771469105805170867187811695413879850542054000336443496598444181875}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{35}+\frac{2340152978353774612886293491772624917167116549480248454438471417398294145578977980012267179996126805553389951607219345625}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{33}-\frac{33209040528286985412165288509882572289126686451407684975188887340150559047921168543941385010538740277954330174455258590000}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^{31}+\frac{772781589551746179614393733869947633571187692273581920907845017098874111533973979212856669463074516638557722256072912786875}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^{29}-\frac{29351705821549109945130204832188445620551177113720889836275291919487656822974525638057637712540236785163949600043021118193125}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{27}+\frac{452119767326125705215553912363776054402515741773757581795471423254466867005331716671499050427906840929897106069517195250784375}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{25}-\frac{2802304948338281798772379582349043271609327954873932778184413845648151567906232922254667376898546070074395441169401296276656250}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^{23}+\frac{27684275245083867525152899473931061589996571329917085988949202208337612114017526527813168726053692562358036812341463671018953125}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^{21}-\frac{430659646488430189711865624051208912312658952708388453302982847923401240983636462900423442312850835991624236367252446226160328125}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{19}+\frac{2597587219698270978352310555292548320324132965764685092579536249681553965794764649569804318126344523810624873329283683687185984375}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{17}-\frac{5959035681127417363221114155333294806103510376983194431170828005656551296221434468152505799122819832006245033987102749909736250000}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^{15}+\frac{20282628310618264616260192516998968006283198590280859540938420932034999832354366282421162762872700516658636388860755387947344609375}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^{13}-\frac{99031694638442722576733108535488769125703640039515760609322609337074044874343407437706952754854627166842850596400590795598934015625}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^{11}+\frac{165411921160853798955631429309157981130339679849914337920417516469335835787531409780824743540613107172873002252329133018919389171875}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^9-\frac{88163620056482861324495796113300036236002567439004925546999855016289482266728841514717837973421670349596512994219007479414093406250}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^7+\frac{53715951728280908639906399173428096683880089826235484661751897627190437405315563344903103650338456678878038272959463275378783515625}{311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081}\cdot t^5-\frac{30705653516209711921362997898995933601514035403032128828846563247689347693802819923755101415679317940194753343983125275883297890625}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\cdot t^3+\frac{2611712053686638207598833125877332311503732718409969748444503409908438723489136389598145915786783089688252659346461790427988671875}{623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162}\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.