Rule: Q[4, 63]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{67}-\frac{83322607446377572467858913592741841096986281702031816791416}{5007268306082155904346097000111886187164809621515616675}\cdot t^{65}+\frac{2400336898339731219876869223233519799955153342026377759706138792}{295428830058847198356419723006601285042723767669421383825}\cdot t^{63}-\frac{732141089716224228622597116751437047454763529161318789945647274068}{295428830058847198356419723006601285042723767669421383825}\cdot t^{61}+\frac{31319634532143738568874333214754318142131681003391610710716409628462}{59085766011769439671283944601320257008544753533884276765}\cdot t^{59}-\frac{84730622390191736740574241248032943467284136157238419162179901863113}{1001453661216431180869219400022377237432961924303123335}\cdot t^{57}+\frac{20973532307860579298535079866035023974473764303000533125985954579711939}{2002907322432862361738438800044754474865923848606246670}\cdot t^{55}-\frac{4129472372348864526336447678599121730897551786798474234620805221864905179}{4005814644865724723476877600089508949731847697212493340}\cdot t^{53}+\frac{658272483385361161117937559701290038791019046697137414748973989771063221347}{8011629289731449446953755200179017899463695394424986680}\cdot t^{51}-\frac{17207376759205676633667604479441650956061507555457340085630456027004070334955}{3204651715892579778781502080071607159785478157769994672}\cdot t^{49}+\frac{1860727761696482809474988784885063358409621654640519891175241971196966137307235}{6409303431785159557563004160143214319570956315539989344}\cdot t^{47}-\frac{167533839826120685280534156557703347580344167951737162345168348403337245493753235}{12818606863570319115126008320286428639141912631079978688}\cdot t^{45}+\frac{12613310085152745214434097177752431562066354759751259873243016640686574213348867485}{25637213727140638230252016640572857278283825262159957376}\cdot t^{43}-\frac{796109474575552551847097623145328823580616224569673292474911665404844698209281488705}{51274427454281276460504033281145714556567650524319914752}\cdot t^{41}+\frac{42169917970195794285788866640445459157065017803017694629706755841781520376615591686675}{102548854908562552921008066562291429113135301048639829504}\cdot t^{39}-\frac{1874172431551510872507968644013560536083483888259765970629443098612037013705661084736475}{205097709817125105842016133124582858226270602097279659008}\cdot t^{37}+\frac{34890519371712794235075551917087707675877075844766824846152470399603137541910733871144225}{205097709817125105842016133124582858226270602097279659008}\cdot t^{35}-\frac{1085328683502808536768046504567260061200547295088600461587109059472499982104416018653524225}{410195419634250211684032266249165716452541204194559318016}\cdot t^{33}+\frac{56185007829097307119738824996497000997421220696611138941881227624790071372918525092985096725}{1640781678537000846736129064996662865810164816778237272064}\cdot t^{31}-\frac{1203592334728014143083624837198110330088276013594991653196930834047043513411173907277804915125}{3281563357074001693472258129993325731620329633556474544128}\cdot t^{29}+\frac{21191537156337494527226013102310983470081853699848832726740038261796597014936210302077519215875}{6563126714148003386944516259986651463240659267112949088256}\cdot t^{27}-\frac{304023452102445701328207707465522151762913191760712014568213979235045184416024150199495426919375}{13126253428296006773889032519973302926481318534225898176512}\cdot t^{25}+\frac{3516068389265075727416783003949432144185280658865214339652150437643785134798915231173459430743125}{26252506856592013547778065039946605852962637068451796353024}\cdot t^{23}-\frac{32349914413035937543177017905925972450508544369138382989151483999978901834314833724874142277748125}{52505013713184027095556130079893211705925274136903592706048}\cdot t^{21}+\frac{232951286826362727210073243688656069381173063628486432011448863875800020023609309413447571995490625}{105010027426368054191112260159786423411850548273807185412096}\cdot t^{19}-\frac{1286536896889023181618108486132322842337241645941658779682774975157990530028100476305838947607528125}{210020054852736108382224520319572846823701096547614370824192}\cdot t^{17}+\frac{5312330850576991740266781333163711503397178736997919567156885985969837451606424728979671191868250625}{420040109705472216764449040639145693647402193095228741648384}\cdot t^{15}-\frac{15877938083364891602641763055043170876232787704269853386623199940407687376157889094332964145396600625}{840080219410944433528898081278291387294804386190457483296768}\cdot t^{13}+\frac{32947201686175199983671440703490836671028443465183481551919005931197324025131629777655141272380039375}{1680160438821888867057796162556582774589608772380914966593536}\cdot t^{11}-\frac{44943836224568244497553408177343977616640020095373517811279891668737465454749527287166278955020746875}{3360320877643777734115592325113165549179217544761829933187072}\cdot t^9+\frac{37512513739735277803169275531060296226141388267733806374914585882652917776422260758805988728748040625}{6720641755287555468231184650226331098358435089523659866374144}\cdot t^7-\frac{17425269856275595647745040180507813464387273582644125949364467334489824931438315521451854538324715625}{13441283510575110936462369300452662196716870179047319732748288}\cdot t^5+\frac{7859806530028783366511497266118875521783013885525938720071165757108952180823568615460391367330540625}{53765134042300443745849477201810648786867480716189278930993152}\cdot t^3-\frac{617213899503470314448637907924355289960163446852576800089626660714753737514023354876117167702153125}{107530268084600887491698954403621297573734961432378557861986304}\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 (physicists') type can be downloaded here packed into a single file.