Rule: Q[2, 84, 87]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{86}-85\cdot t^{84}+\frac{1743}{2}\cdot t^{82}-\frac{91881}{16}\cdot t^{80}+\frac{437265}{16}\cdot t^{78}-\frac{6405399}{64}\cdot t^{76}+\frac{37562525}{128}\cdot t^{74}-\frac{2898753715}{4096}\cdot t^{72}+\frac{23446881315}{16384}\cdot t^{70}-\frac{161322559475}{65536}\cdot t^{68}+\frac{477263364265}{131072}\cdot t^{66}-\frac{4898229264825}{1048576}\cdot t^{64}+\frac{1371504194151}{262144}\cdot t^{62}-\frac{5391921894261}{1048576}\cdot t^{60}+\frac{9338260032135}{2097152}\cdot t^{58}-\frac{114341806171253}{33554432}\cdot t^{56}+\frac{620022470083555}{268435456}\cdot t^{54}-\frac{1491180091915239}{1073741824}\cdot t^{52}+\frac{1592032851754917}{2147483648}\cdot t^{50}-\frac{6037895490401775}{17179869184}\cdot t^{48}+\frac{2541323176557165}{17179869184}\cdot t^{46}-\frac{3795482666286675}{68719476736}\cdot t^{44}+\frac{2510857763851185}{137438953472}\cdot t^{42}-\frac{93993414551124795}{17592186044416}\cdot t^{40}+\frac{96977332473382725}{70368744177664}\cdot t^{38}-\frac{87967825456500717}{281474976710656}\cdot t^{36}+\frac{34943083251951735}{562949953421312}\cdot t^{34}-\frac{48402641245296107}{4503599627370496}\cdot t^{32}+\frac{3633128035361209}{2251799813685248}\cdot t^{30}-\frac{1879204156221315}{9007199254740992}\cdot t^{28}+\frac{415403024006817}{18014398509481984}\cdot t^{26}-\frac{622147386185325}{288230376151711744}\cdot t^{24}+\frac{780512175396135}{4611686018427387904}\cdot t^{22}-\frac{202355008436035}{18446744073709551616}\cdot t^{20}+\frac{21335988680825}{36893488147419103232}\cdot t^{18}-\frac{7174519270695}{295147905179352825856}\cdot t^{16}+\frac{234461414075}{295147905179352825856}\cdot t^{14}-\frac{23065933709}{1180591620717411303424}\cdot t^{12}+\frac{817589487}{2361183241434822606848}\cdot t^{10}-\frac{314457495}{75557863725914323419136}\cdot t^8+\frac{9366819}{302231454903657293676544}\cdot t^6-\frac{148995}{1208925819614629174706176}\cdot t^4+\frac{473}{2417851639229258349412352}\cdot t^2-\frac{1}{19342813113834066795298816}$
• $P_3$:
  $4\cdot t^{173}-172\cdot t^{171}+\frac{14535}{4}\cdot t^{169}-\frac{100555}{2}\cdot t^{167}+\frac{16397563}{32}\cdot t^{165}-\frac{131277531}{32}\cdot t^{163}+\frac{27512019711}{1024}\cdot t^{161}-\frac{18945402795}{128}\cdot t^{159}+\frac{2867147042265}{4096}\cdot t^{157}-\frac{11821913360127}{4096}\cdot t^{155}+\frac{688266029039589}{65536}\cdot t^{153}-\frac{1115889206033511}{32768}\cdot t^{151}+\frac{52005947565142025}{524288}\cdot t^{149}-\frac{136984610093945525}{524288}\cdot t^{147}+\frac{41999481454803697965}{67108864}\cdot t^{145}-\frac{22980848343194476245}{16777216}\cdot t^{143}+\frac{2953475357322196421715}{1073741824}\cdot t^{141}-\frac{5460996960803686527225}{1073741824}\cdot t^{139}+\frac{149220575074268254936225}{17179869184}\cdot t^{137}-\frac{118008393666543553733945}{8589934592}\cdot t^{135}+\frac{2772430962893211541619565}{137438953472}\cdot t^{133}-\frac{3787176936239746484957445}{137438953472}\cdot t^{131}+\frac{154295749340102590045036575}{4398046511104}\cdot t^{129}-\frac{5731111910415558340284975}{137438953472}\cdot t^{127}+\frac{203798339534377254580533711}{4398046511104}\cdot t^{125}-\frac{212004984079385734630756545}{4398046511104}\cdot t^{123}+\frac{3307013296356821552878516335}{70368744177664}\cdot t^{121}-\frac{1512277433330216961066895225}{35184372088832}\cdot t^{119}+\frac{20778277611372707013015012475}{562949953421312}\cdot t^{117}-\frac{16765920555383494624294872135}{562949953421312}\cdot t^{115}+\frac{814078586966954127868539902555}{36028797018963968}\cdot t^{113}-\frac{145259680191937901002484787485}{9007199254740992}\cdot t^{111}+\frac{12490286585518040642537600388675}{1152921504606846976}\cdot t^{109}-\frac{7900045867435975416073105081425}{1152921504606846976}\cdot t^{107}+\frac{75296067418872969049664838515565}{18446744073709551616}\cdot t^{105}-\frac{21126234743424789877244091382065}{9223372036854775808}\cdot t^{103}+\frac{178705492926264768478523690869545}{147573952589676412928}\cdot t^{101}-\frac{89017827902706360309384951557625}{147573952589676412928}\cdot t^{99}+\frac{1336921000483060538268812383919625}{4722366482869645213696}\cdot t^{97}-\frac{73892499741798787585227806974475}{590295810358705651712}\cdot t^{95}+\frac{984865705513825631546394501913525}{18889465931478580854784}\cdot t^{93}-\frac{386324545038340918004353170657075}{18889465931478580854784}\cdot t^{91}+\frac{2282826857044741788207541462973625}{302231454903657293676544}\cdot t^{89}-\frac{396749066757820381795700886250875}{151115727451828646838272}\cdot t^{87}+\frac{2075857704532875592024779042607725}{2417851639229258349412352}\cdot t^{85}-\frac{638312834210367430105810610000825}{2417851639229258349412352}\cdot t^{83}+\frac{94442546731212189767394500253600325}{1237940039285380274899124224}\cdot t^{81}-\frac{6407979799990105018561697537729625}{309485009821345068724781056}\cdot t^{79}+\frac{104460242136346632604172434464259125}{19807040628566084398385987584}\cdot t^{77}-\frac{24951074978853081387739472917748751}{19807040628566084398385987584}\cdot t^{75}+\frac{89340945892022323678680048189358431}{316912650057057350374175801344}\cdot t^{73}-\frac{9357086155118550399632200169043279}{158456325028528675187087900672}\cdot t^{71}+\frac{29322016513833036246010110239687955}{2535301200456458802993406410752}\cdot t^{69}-\frac{5363281673277117030495845830524555}{2535301200456458802993406410752}\cdot t^{67}+\frac{29279545134853594455373617608122941}{81129638414606681695789005144064}\cdot t^{65}-\frac{290782342821311480458255942632237}{5070602400912917605986812821504}\cdot t^{63}+\frac{1375055485544845814370396745667697}{162259276829213363391578010288128}\cdot t^{61}-\frac{188660334274034176060715702846895}{162259276829213363391578010288128}\cdot t^{59}+\frac{383826197316138496123525050619545}{2596148429267413814265248164610048}\cdot t^{57}-\frac{22571356334434673537698820220663}{1298074214633706907132624082305024}\cdot t^{55}+\frac{39202882054544432986529529856941}{20769187434139310514121985316880384}\cdot t^{53}-\frac{3918582001389977415888415214193}{20769187434139310514121985316880384}\cdot t^{51}+\frac{23023926505862770531141610129475}{1329227995784915872903807060280344576}\cdot t^{49}-\frac{483986443066184365519493306025}{332306998946228968225951765070086144}\cdot t^{47}+\frac{9512533544628096347755859342055}{85070591730234615865843651857942052864}\cdot t^{45}-\frac{664601849624687041939188479085}{85070591730234615865843651857942052864}\cdot t^{43}+\frac{673552716286298988631972162305}{1361129467683753853853498429727072845824}\cdot t^{41}-\frac{19260469638539725578121675725}{680564733841876926926749214863536422912}\cdot t^{39}+\frac{15840186461884502389997959725}{10889035741470030830827987437816582766592}\cdot t^{37}-\frac{728058259738790793080651565}{10889035741470030830827987437816582766592}\cdot t^{35}+\frac{952076185812264883259313585}{348449143727040986586495598010130648530944}\cdot t^{33}-\frac{4296255180063549999665985}{43556142965880123323311949751266331066368}\cdot t^{31}+\frac{4352415378495753267635475}{1393796574908163946345982392040522594123776}\cdot t^{29}-\frac{119834575048777690672725}{1393796574908163946345982392040522594123776}\cdot t^{27}+\frac{45472363072563210190407}{22300745198530623141535718272648361505980416}\cdot t^{25}-\frac{459316798712759698893}{11150372599265311570767859136324180752990208}\cdot t^{23}+\frac{124819710069095815059}{178405961588244985132285746181186892047843328}\cdot t^{21}-\frac{1754728820090381655}{178405961588244985132285746181186892047843328}\cdot t^{19}+\frac{2564603660132096265}{22835963083295358096932575511191922182123945984}\cdot t^{17}-\frac{5809228810425801}{5708990770823839524233143877797980545530986496}\cdot t^{15}+\frac{2595612872743443}{365375409332725729550921208179070754913983135744}\cdot t^{13}-\frac{13438059476569}{365375409332725729550921208179070754913983135744}\cdot t^{11}+\frac{783768050065}{5846006549323611672814739330865132078623730171904}\cdot t^9-\frac{933921945}{2923003274661805836407369665432566039311865085952}\cdot t^7+\frac{20753821}{46768052394588893382517914646921056628989841375232}\cdot t^5-\frac{13717}{46768052394588893382517914646921056628989841375232}\cdot t^3+\frac{87}{1496577676626844588240573268701473812127674924007424}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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