Rule: Q[2, 92, 95]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{94}-47\cdot t^{92}+\frac{4277}{8}\cdot t^{90}-\frac{62745}{16}\cdot t^{88}+\frac{1334377}{64}\cdot t^{86}-\frac{10959883}{128}\cdot t^{84}+\frac{578881093}{2048}\cdot t^{82}-\frac{3156755517}{4096}\cdot t^{80}+\frac{28998103005}{16384}\cdot t^{78}-\frac{113831769051}{32768}\cdot t^{76}+\frac{1544859722835}{262144}\cdot t^{74}-\frac{4570280516295}{524288}\cdot t^{72}+\frac{23743164633435}{2097152}\cdot t^{70}-\frac{54453696666425}{4194304}\cdot t^{68}+\frac{1772078871515945}{134217728}\cdot t^{66}-\frac{3207687071225065}{268435456}\cdot t^{64}+\frac{5181648345825105}{536870912}\cdot t^{62}-\frac{7485482828078895}{1073741824}\cdot t^{60}+\frac{38740656741811825}{8589934592}\cdot t^{58}-\frac{44939161820501717}{17179869184}\cdot t^{56}+\frac{93522039464287357}{68719476736}\cdot t^{54}-\frac{87299438012651799}{137438953472}\cdot t^{52}+\frac{584641690933213563}{2199023255552}\cdot t^{50}-\frac{438570772439183475}{4398046511104}\cdot t^{48}+\frac{588937894418332095}{17592186044416}\cdot t^{46}-\frac{353362736650999257}{35184372088832}\cdot t^{44}+\frac{756292192017749541}{281474976710656}\cdot t^{42}-\frac{359959965355048289}{562949953421312}\cdot t^{40}+\frac{303862308416599205}{2251799813685248}\cdot t^{38}-\frac{113323715022211799}{4503599627370496}\cdot t^{36}+\frac{2379798015466447779}{576460752303423488}\cdot t^{34}-\frac{683597893843664723}{1152921504606846976}\cdot t^{32}+\frac{683597893843664723}{9223372036854775808}\cdot t^{30}-\frac{147722346657721885}{18446744073709551616}\cdot t^{28}+\frac{109488327522782103}{147573952589676412928}\cdot t^{26}-\frac{17231819101648515}{295147905179352825856}\cdot t^{24}+\frac{4555538383194435}{1180591620717411303424}\cdot t^{22}-\frac{498970775968665}{2361183241434822606848}\cdot t^{20}+\frac{356407697120475}{37778931862957161709568}\cdot t^{18}-\frac{25422087486915}{75557863725914323419136}\cdot t^{16}+\frac{2824676387435}{302231454903657293676544}\cdot t^{14}-\frac{118290635645}{604462909807314587353088}\cdot t^{12}+\frac{14298868045}{4835703278458516698824704}\cdot t^{10}-\frac{293410425}{9671406556917033397649408}\cdot t^8+\frac{7468629}{38685626227668133590597632}\cdot t^6-\frac{50807}{77371252455336267181195264}\cdot t^4+\frac{2209}{2475880078570760549798248448}\cdot t^2-\frac{1}{4951760157141521099596496896}$
• $P_3$:
  $2\cdot t^{189}-95\cdot t^{187}+\frac{4441}{2}\cdot t^{185}-\frac{136183}{4}\cdot t^{183}+\frac{49298431}{128}\cdot t^{181}-\frac{877624293}{256}\cdot t^{179}+\frac{1600348605}{64}\cdot t^{177}-\frac{78691795809}{512}\cdot t^{175}+\frac{13311279197645}{16384}\cdot t^{173}-\frac{122926169740715}{32768}\cdot t^{171}+\frac{1003725424669715}{65536}\cdot t^{169}-\frac{7317967974178225}{131072}\cdot t^{167}+\frac{1536797592240647555}{8388608}\cdot t^{165}-\frac{9139208904424011257}{16777216}\cdot t^{163}+\frac{24765635937419636337}{16777216}\cdot t^{161}-\frac{61457306766094267587}{16777216}\cdot t^{159}+\frac{8975834206279996141125}{1073741824}\cdot t^{157}-\frac{37809381879265118705739}{2147483648}\cdot t^{155}+\frac{147460636758598755544953}{4294967296}\cdot t^{153}-\frac{533969377791236913824991}{8589934592}\cdot t^{151}+\frac{28794583135193409573921585}{274877906944}\cdot t^{149}-\frac{90525002255076100879928475}{549755813888}\cdot t^{147}+\frac{66495691106047909282169565}{274877906944}\cdot t^{145}-\frac{365837096820590785175682645}{1099511627776}\cdot t^{143}+\frac{15098108547328919850583333215}{35184372088832}\cdot t^{141}-\frac{36566854522119881394368958297}{70368744177664}\cdot t^{139}+\frac{83260430492907290374740336565}{140737488355328}\cdot t^{137}-\frac{178424303430523110336020013327}{281474976710656}\cdot t^{135}+\frac{23053669244921881755425270793479}{36028797018963968}\cdot t^{133}-\frac{43884992424181681167076058571733}{72057594037927936}\cdot t^{131}+\frac{39415574116827840277632511031807}{72057594037927936}\cdot t^{129}-\frac{8357217798407461238893384341595}{18014398509481984}\cdot t^{127}+\frac{857209350188386212112722747709281}{2305843009213693952}\cdot t^{125}-\frac{1298728807776420973527559839268575}{4611686018427387904}\cdot t^{123}+\frac{1860926802961403718862494145907025}{9223372036854775808}\cdot t^{121}-\frac{2522794896653218110186623577453775}{18446744073709551616}\cdot t^{119}+\frac{51788140381138032664604602332647875}{590295810358705651712}\cdot t^{117}-\frac{62898603754379585000851718505855025}{1180591620717411303424}\cdot t^{115}+\frac{4520582148109338778728933370193495}{147573952589676412928}\cdot t^{113}-\frac{39379976202217995987721215437953345}{2361183241434822606848}\cdot t^{111}+\frac{649732953102528191374328051564120065}{75557863725914323419136}\cdot t^{109}-\frac{634496833439481054675144035323416375}{151115727451828646838272}\cdot t^{107}+\frac{586762645017174627497141275523178615}{302231454903657293676544}\cdot t^{105}-\frac{513800045794502130233750965309215405}{604462909807314587353088}\cdot t^{103}+\frac{13630501783044598768896809399551483245}{38685626227668133590597632}\cdot t^{101}-\frac{10696215991234853729952575987017061175}{77371252455336267181195264}\cdot t^{99}+\frac{3971556625769053938429127029974980875}{77371252455336267181195264}\cdot t^{97}-\frac{1395090094114101469424280739245522075}{77371252455336267181195264}\cdot t^{95}+\frac{29660598677703634386126608350454151975}{4951760157141521099596496896}\cdot t^{93}-\frac{18628818031162418737719035638171926825}{9903520314283042199192993792}\cdot t^{91}+\frac{11055174505147357981842360795070087755}{19807040628566084398385987584}\cdot t^{89}-\frac{6195737754664172865522708661422679725}{39614081257132168796771975168}\cdot t^{87}+\frac{52436530640454666534004455443414531655}{1267650600228229401496703205376}\cdot t^{85}-\frac{26161823419084467292852184900366619565}{2535301200456458802993406410752}\cdot t^{83}+\frac{3075720664644587818627701042453726845}{1267650600228229401496703205376}\cdot t^{81}-\frac{2724476369547386502294744168992779095}{5070602400912917605986812821504}\cdot t^{79}+\frac{18168047068228450276863009433622730225}{162259276829213363391578010288128}\cdot t^{77}-\frac{7118883627198973912002810798982739895}{324518553658426726783156020576256}\cdot t^{75}+\frac{2619865588399650961571372929698952275}{649037107316853453566312041152512}\cdot t^{73}-\frac{904561550205420021963906561662482425}{1298074214633706907132624082305024}\cdot t^{71}+\frac{74923616870397507141429811201366400925}{664613997892457936451903530140172288}\cdot t^{69}-\frac{22687605265152503794941087356218656375}{1329227995784915872903807060280344576}\cdot t^{67}+\frac{3210411035177882942626169336712911025}{1329227995784915872903807060280344576}\cdot t^{65}-\frac{211977072056119410563278745359462521}{664613997892457936451903530140172288}\cdot t^{63}+\frac{6676900586365526344824128737283283891}{170141183460469231731687303715884105728}\cdot t^{61}-\frac{1528209859590096685445416873322151597}{340282366920938463463374607431768211456}\cdot t^{59}+\frac{324716759954203397155459293022416075}{680564733841876926926749214863536422912}\cdot t^{57}-\frac{63922371942984305941243081046770437}{1361129467683753853853498429727072845824}\cdot t^{55}+\frac{186116390301291014128853881389457989}{43556142965880123323311949751266331066368}\cdot t^{53}-\frac{31232967294899840969480899006194183}{87112285931760246646623899502532662132736}\cdot t^{51}+\frac{602599622990545459040929766397045}{21778071482940061661655974875633165533184}\cdot t^{49}-\frac{341214450684677616486803559822675}{174224571863520493293247799005065324265472}\cdot t^{47}+\frac{706574666971780812549924796892655}{5575186299632655785383929568162090376495104}\cdot t^{45}-\frac{83319760169485722488319304135545}{11150372599265311570767859136324180752990208}\cdot t^{43}+\frac{8918147348427791601995494753665}{22300745198530623141535718272648361505980416}\cdot t^{41}-\frac{862828021448952947147018995659}{44601490397061246283071436545296723011960832}\cdot t^{39}+\frac{2403456480203199075261028106685}{2854495385411919762116571938898990272765493248}\cdot t^{37}-\frac{187271736229204503721196917383}{5708990770823839524233143877797980545530986496}\cdot t^{35}+\frac{6493029361817415900229621287}{5708990770823839524233143877797980545530986496}\cdot t^{33}-\frac{199055027364278309464224537}{5708990770823839524233143877797980545530986496}\cdot t^{31}+\frac{342797609144517353036167587}{365375409332725729550921208179070754913983135744}\cdot t^{29}-\frac{16057223958369926983961485}{730750818665451459101842416358141509827966271488}\cdot t^{27}+\frac{648385517302490884694687}{1461501637330902918203684832716283019655932542976}\cdot t^{25}-\frac{22318377012350198248105}{2923003274661805836407369665432566039311865085952}\cdot t^{23}+\frac{10341080702093086649935}{93536104789177786765035829293842113257979682750464}\cdot t^{21}-\frac{248030169246630517285}{187072209578355573530071658587684226515959365500928}\cdot t^{19}+\frac{1208696994485955975}{93536104789177786765035829293842113257979682750464}\cdot t^{17}-\frac{37412881206532755}{374144419156711147060143317175368453031918731001856}\cdot t^{15}+\frac{7142055131332401}{11972621413014756705924586149611790497021399392059392}\cdot t^{13}-\frac{63221971128407}{23945242826029513411849172299223580994042798784118784}\cdot t^{11}+\frac{394219014059}{47890485652059026823698344598447161988085597568237568}\cdot t^9-\frac{1607690225}{95780971304118053647396689196894323976171195136475136}\cdot t^7+\frac{244634671}{12259964326927110866866776217202473468949912977468817408}\cdot t^5-\frac{276877}{24519928653854221733733552434404946937899825954937634816}\cdot t^3+\frac{47}{24519928653854221733733552434404946937899825954937634816}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.