Rule: Q[17, 36]

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.

• $P_1$:
  $\frac{583401555}{32768}\cdot t^{17}-\frac{300540195}{4096}\cdot t^{15}+\frac{1017958725}{8192}\cdot t^{13}-\frac{456326325}{4096}\cdot t^{11}+\frac{929553625}{16384}\cdot t^9-\frac{66927861}{4096}\cdot t^7+\frac{20369349}{8192}\cdot t^5-\frac{692835}{4096}\cdot t^3+\frac{109395}{32768}\cdot t$
• $P_2$:
  $\frac{583401555}{32768}\cdot t^{53}-\frac{15393489633141207022646586270197259140074297756592878552347104004957698552347093644006585}{64693374941195468683519650717089642801532261294556272823529903841201215338139533312}\cdot t^{51}+\frac{153938063085752343323711673789394619330989284766598312273708074141484676035247617537788073805}{102603692656736013332062166037304173483230166413166248698118427492145127526289299832832}\cdot t^{49}-\frac{1902800004937810883978483052111168236743177834232667236145898757883099155619294725248638189729}{320636539552300041662694268866575542135094270041144527181620085912953523519654061977600}\cdot t^{47}+\frac{103734383656519439045386092922905688985225499068268016386792605592706745330648973660681947925081859}{6280628536750453216088855338558481719342226561565938998433574242862933618702983766017228800}\cdot t^{45}-\frac{626335638347882535835427121838612564942415876275008669120492542840037829827685631481774222938820177}{18213822756576314326657680481819596986092457028541223095457365304302507494238652921449963520}\cdot t^{43}+\frac{1759764444893787155376477808355464007121902378369665559075400902538426196714313165474488548028704009759}{31655623950929634299731048677402459561828690315604645739904900898877758024986778777480036597760}\cdot t^{41}-\frac{1244614959992836076236478658944877367096338619868224437111727147586175515796623453772441647802550885543}{17410593173011298864852076772571352759005779673582555156947695494382766913742728327614020128768}\cdot t^{39}+\frac{99534243344259097342065664875176063755656341547222981767599869497730678182649202590382165948999411238649}{1339276397923946066527082828659334827615829205660196550534438114952520531826363717508770779136000}\cdot t^{37}-\frac{3086880081144986191070286663208390984257991216654702990787691339748976093195024242118758952017902283233917}{48883588524224031428238523246065721207977766006597174094506991195766999411662275689070133438464000}\cdot t^{35}+\frac{2590241242051982287795685741342688179150425513792993343517989262186997956988201666319468826842197370343739}{58660306229068837713886227895278865449573319207916608913408389434920399293994730826884160126156800}\cdot t^{33}-\frac{2834065367332863507688849612224752222977740508489447126163497450274809749403353333237852328092221216477}{111099064827781889609633007377422093654494922742266304760243161808561362299232444747886666905600}\cdot t^{31}+\frac{859322245231539546554683024377404102597054202039127649223312221201592259073733408630715969175641484611}{70490441132109888579905080542916087008369192360610345089257730250949278148478516667624643829760}\cdot t^{29}-\frac{38177113769072607864421288945982992861620395972471941531813273652282941086621647136096097807101803083781}{7930174627362362465239321561078059788441534140568663822541494653231793791703833125107772430848000}\cdot t^{27}+\frac{2759415508965111253619787925392863218922762438650143772316869898295664941189372962516296864635013005531}{1762261028302747214497627013572902175209229809015258627231443256273731953711962916690616095744000}\cdot t^{25}-\frac{253436164689622843098936230896005577319399874154820733063467067742792744242788674879669809574426773669}{607596954540903713520268792071004967365617060238739170171536740097856277953733301276373288663040}\cdot t^{23}+\frac{315309468330669784338507512000186647305388682792907540740448336759589897291716450367962690110935495499833}{3493572016436643461157269141900629288721867984179979548637214157973564897092520349011641614669086720}\cdot t^{21}-\frac{1145331441252036727997050771302609978904793127285276215347472769368302799712774275975328755674577988575829}{73015655143525848338186925065723152134287040869361572566517775901647506349233675294343309746583912448}\cdot t^{19}+\frac{64749767088007621758430553798471135797805083048655950891362624953456857235291009803997924229996052530098451}{30013277193207203974802099198068306219409567852090204302342306831150896030921842318359013111622124011520}\cdot t^{17}-\frac{863759868915112144604688253501751699736847013001627994052405051736932086406515083465256457660437480942829}{3751659649150900496850262399758538277426195981511275537792788353893862003865230289794876638952765501440}\cdot t^{15}+\frac{913971434928435715483139836655549939914576785401201871091447158856843593999303973499679915094385974203}{49202093759356072089839506882079190523622242380475744757938207919919501690035807079277070674790367232}\cdot t^{13}-\frac{126286395565538837253691095991854931729519263405186706155629719787380432251482891763364680508828881417}{115435681512335399903084996915647331613113722508039247316701180119811138580468624301380819660085092352}\cdot t^{11}+\frac{2820052487794530836375177674737463040540460988832470948016121859240834606218136537754205995112327835}{62964917188546581765319089226716726334425666822566862172746098247169711952982885982571356178228232192}\cdot t^9-\frac{155693203321087070168905346408816453869931676634855807265164127342150261342979484816922529859462107}{131176910809472045344414769222326513196720139213680962859887704681603566568714345797023658704642150400}\cdot t^7+\frac{19099544162738238054603283005741024332390908515502200000210800702108924430483743267890622251383927}{1049415286475776362755318153778612105573761113709447702879101637452828532549714766376189269637137203200}\cdot t^5-\frac{235178426639267852665076570276694133699778935347546176741596528788791375031783026474665087349}{1778669977077587055517488396234935772158917141880419835388307860089539885677482654874897067181588480}\cdot t^3+\frac{60350314728665122656123465879737368057552665745785946066208532390834455589157239013546894623}{209883057295155272551063630755722421114752222741889540575820327490565706509942953275237853927427440640}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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