Rule: Q[1, 2, 10, 28]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{13}-\frac{124943}{42780}\cdot t^{11}+\frac{576433}{179676}\cdot t^9-\frac{310453}{189658}\cdot t^7+\frac{10439}{27094}\cdot t^5-\frac{97669}{2763588}\cdot t^3+\frac{3421}{4605980}\cdot t$
• $P_4$:
  $t^{41}-\frac{3456646554674717718481692338548395717412232611661359053764791118911771492181232687616018083462907}{354061146769560851912972996661228874481944839595474445190507162376531917503490972230972649042220}\cdot t^{39}+\frac{501454589137974068758840198003462860691411299459604496571000886958587847584884967939419066963849207}{11400768925979859431597730492491569758318623834974277135134330628524327743612409305837319299159484}\cdot t^{37}-\frac{4168954584765809634200978775452733472837192058289966520349919446764307128144800458781526572832399971047}{34373318311829276186267157434862082821330650862447445562430006845000848146991414057099517686965844260}\cdot t^{35}+\frac{38442989873646214590258593927541266188224858042873131312645807715538940123907097887938950440018257352067}{167938212323508749367190969181754747498501179927957519747872319157004143803872337250400500699175981956}\cdot t^{33}-\frac{772811599226830611123593701442558983598795698947402929184799088351654749877905551346424493529177435785385}{2466578664597357919312388836226490759455094240503146825783061457025682403280128916446840819063556064361}\cdot t^{31}+\frac{520619819193051449257774556234933934567384811056181443326357513553756546862024823516666914835145311575598621}{1619587377996103885406570153593232884151885266627146891574652127669605332863452390137917576517376893228005}\cdot t^{29}-\frac{202318779576283135710778756140993316682685640079491083141525540949367371348319421283754262227602018441813253}{802752004745894969288473902215776299101369219110846720171784098062326121506232923807489581404265068817359}\cdot t^{27}+\frac{521646679859420079801992028648847428429512011591640144886104271350368050026451417385242166620545363946062827}{3419128909102885980302759213141269422098424451768421215546487825080277924933955045846714883758906774592455}\cdot t^{25}-\frac{29788362357014150204855959856253938104501390358462859107292563112693261963305687632819270877838795682434805}{416241780238612206297727208556328451385895150650068669718702865661946877818046701233513116283692998646038}\cdot t^{23}+\frac{551078655869834906818009425843816394231915525037905280073902807090882629623021737015258261095055288176713415}{21228330792169222521184087636372751020680652683153502155653846148759290768720381762909168930468342930947938}\cdot t^{21}-\frac{384585060349139063631085584742040707304260227575651666792686326579200697893699371259413807003574706843047}{53203836571852688023017763499681080252332462865046371317428185836489450548171382864434007344532187796862}\cdot t^{19}+\frac{16127621345662525498212626755387536630706072195999932391945350783197131528036794785338316470282094927735}{10575310844924198272933557758298776812939593733652046893929401029398326002846830042642207534457186117254}\cdot t^{17}-\frac{193348719226231579145408843571869870823010087779315566643676733580110913759484999074428413548754914575167}{809011279636701167879417168509856426189878920624381587385599178748971939217782498262128876385974737969931}\cdot t^{15}+\frac{349013139762376423279730374023831514882725617129305034330978937597958529064870275869439771445659298183231415}{12906156944044293731180342089237739567007138420720759463562463698582349346341284194775741964985454994834309243}\cdot t^{13}-\frac{11736993611451575797873488071986059456963312617890944478498547127710077196725459748210945265714850955021585}{5531210118876125884791575181101888385860202180308896912955341585106721148431978940618175127850909283500418247}\cdot t^{11}+\frac{8052638350065734836657056264992746481687588617025371117289961886465132236249485938011475900919205407507116}{73917080679526409551305595601997962974677247318673440564039564819153455347227354933715613072189424061323771119}\cdot t^9-\frac{110164715182833300805590006485901326425824453279432683098093331176988924706993524767763180957426252426495}{32852035857567293133913598045332427988745443252743751361795362141845980154323268859429161365417521805032787164}\cdot t^7+\frac{13278316249412271840519747362387134513887980900249856538229953309774983860235435530866955684754279979}{247007788402761602510628556731822766832672505659727453848085429637939700408445630522023769664793397030321708}\cdot t^5-\frac{79998937645499374403802166187038193420996766538238181048783349472561138074499799302709919164564665}{230810556376351005624685700552686847696103816764007620808866712940369883988219687536973030670380715257841596}\cdot t^3+\frac{69893760127070073653352038263537062339823635227276724806877683480098653045378433476558518473965205}{145487587369226583878760219915043609664444105833579470316522318056746483540574476377472000332563310850859486012}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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