Rule: Q[28, 58, 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.

• $P_1$:
  $268435456\cdot t^{28}-1811939328\cdot t^{26}+5452595200\cdot t^{24}-9646899200\cdot t^{22}+11142168576\cdot t^{20}-8820883456\cdot t^{18}+4889837568\cdot t^{16}-1905131520\cdot t^{14}+515973120\cdot t^{12}-94595072\cdot t^{10}+11202048\cdot t^8-792064\cdot t^6+29120\cdot t^4-420\cdot t^2+1$
• $P_2$:
  $268435456\cdot t^{86}-5704253440\cdot t^{84}+58485374976\cdot t^{82}-385376845824\cdot t^{80}+1834022338560\cdot t^{78}-6716547661824\cdot t^{76}+19693581107200\cdot t^{74}-47493180866560\cdot t^{72}+96038425866240\cdot t^{70}-165194300902400\cdot t^{68}+244358842503680\cdot t^{66}-313486672948800\cdot t^{64}+351105073702656\cdot t^{62}-345083001232704\cdot t^{60}+298824321028320\cdot t^{58}-228683612342506\cdot t^{56}+\frac{620022470083555}{4}\cdot t^{54}-\frac{1491180091915239}{16}\cdot t^{52}+\frac{1592032851754917}{32}\cdot t^{50}-\frac{6037895490401775}{256}\cdot t^{48}+\frac{2541323176557165}{256}\cdot t^{46}-\frac{3795482666286675}{1024}\cdot t^{44}+\frac{2510857763851185}{2048}\cdot t^{42}-\frac{93993414551124795}{262144}\cdot t^{40}+\frac{96977332473382725}{1048576}\cdot t^{38}-\frac{87967825456500717}{4194304}\cdot t^{36}+\frac{34943083251951735}{8388608}\cdot t^{34}-\frac{48402641245296107}{67108864}\cdot t^{32}+\frac{3633128035361209}{33554432}\cdot t^{30}-\frac{1879204156221315}{134217728}\cdot t^{28}+\frac{415403024006817}{268435456}\cdot t^{26}-\frac{622147386185325}{4294967296}\cdot t^{24}+\frac{780512175396135}{68719476736}\cdot t^{22}-\frac{202355008436035}{274877906944}\cdot t^{20}+\frac{21335988680825}{549755813888}\cdot t^{18}-\frac{7174519270695}{4398046511104}\cdot t^{16}+\frac{234461414075}{4398046511104}\cdot t^{14}-\frac{23065933709}{17592186044416}\cdot t^{12}+\frac{817589487}{35184372088832}\cdot t^{10}-\frac{314457495}{1125899906842624}\cdot t^8+\frac{9366819}{4503599627370496}\cdot t^6-\frac{148995}{18014398509481984}\cdot t^4+\frac{473}{36028797018963968}\cdot t^2-\frac{1}{288230376151711744}$
• $P_3$:
  $268435456\cdot t^{173}-11542724608\cdot t^{171}+243856834560\cdot t^{169}-3374065909760\cdot t^{167}+34388182040576\cdot t^{165}-275308936691712\cdot t^{163}+1803027723780096\cdot t^{161}-9932847340584960\cdot t^{159}+46975337140469760\cdot t^{157}-193690228492320768\cdot t^{155}+704784413736539136\cdot t^{153}-2285341093956630528\cdot t^{151}+6656761288338179200\cdot t^{149}-17534030092025027200\cdot t^{147}+41999481454803697965\cdot t^{145}-91923393372777904980\cdot t^{143}+\frac{2953475357322196421715}{16}\cdot t^{141}-\frac{5460996960803686527225}{16}\cdot t^{139}+\frac{149220575074268254936225}{256}\cdot t^{137}-\frac{118008393666543553733945}{128}\cdot t^{135}+\frac{2772430962893211541619565}{2048}\cdot t^{133}-\frac{3787176936239746484957445}{2048}\cdot t^{131}+\frac{154295749340102590045036575}{65536}\cdot t^{129}-\frac{5731111910415558340284975}{2048}\cdot t^{127}+\frac{203798339534377254580533711}{65536}\cdot t^{125}-\frac{212004984079385734630756545}{65536}\cdot t^{123}+\frac{3307013296356821552878516335}{1048576}\cdot t^{121}-\frac{1512277433330216961066895225}{524288}\cdot t^{119}+\frac{20778277611372707013015012475}{8388608}\cdot t^{117}-\frac{16765920555383494624294872135}{8388608}\cdot t^{115}+\frac{814078586966954127868539902555}{536870912}\cdot t^{113}-\frac{145259680191937901002484787485}{134217728}\cdot t^{111}+\frac{12490286585518040642537600388675}{17179869184}\cdot t^{109}-\frac{7900045867435975416073105081425}{17179869184}\cdot t^{107}+\frac{75296067418872969049664838515565}{274877906944}\cdot t^{105}-\frac{21126234743424789877244091382065}{137438953472}\cdot t^{103}+\frac{178705492926264768478523690869545}{2199023255552}\cdot t^{101}-\frac{89017827902706360309384951557625}{2199023255552}\cdot t^{99}+\frac{1336921000483060538268812383919625}{70368744177664}\cdot t^{97}-\frac{73892499741798787585227806974475}{8796093022208}\cdot t^{95}+\frac{984865705513825631546394501913525}{281474976710656}\cdot t^{93}-\frac{386324545038340918004353170657075}{281474976710656}\cdot t^{91}+\frac{2282826857044741788207541462973625}{4503599627370496}\cdot t^{89}-\frac{396749066757820381795700886250875}{2251799813685248}\cdot t^{87}+\frac{2075857704532875592024779042607725}{36028797018963968}\cdot t^{85}-\frac{638312834210367430105810610000825}{36028797018963968}\cdot t^{83}+\frac{94442546731212189767394500253600325}{18446744073709551616}\cdot t^{81}-\frac{6407979799990105018561697537729625}{4611686018427387904}\cdot t^{79}+\frac{104460242136346632604172434464259125}{295147905179352825856}\cdot t^{77}-\frac{24951074978853081387739472917748751}{295147905179352825856}\cdot t^{75}+\frac{89340945892022323678680048189358431}{4722366482869645213696}\cdot t^{73}-\frac{9357086155118550399632200169043279}{2361183241434822606848}\cdot t^{71}+\frac{29322016513833036246010110239687955}{37778931862957161709568}\cdot t^{69}-\frac{5363281673277117030495845830524555}{37778931862957161709568}\cdot t^{67}+\frac{29279545134853594455373617608122941}{1208925819614629174706176}\cdot t^{65}-\frac{290782342821311480458255942632237}{75557863725914323419136}\cdot t^{63}+\frac{1375055485544845814370396745667697}{2417851639229258349412352}\cdot t^{61}-\frac{188660334274034176060715702846895}{2417851639229258349412352}\cdot t^{59}+\frac{383826197316138496123525050619545}{38685626227668133590597632}\cdot t^{57}-\frac{22571356334434673537698820220663}{19342813113834066795298816}\cdot t^{55}+\frac{39202882054544432986529529856941}{309485009821345068724781056}\cdot t^{53}-\frac{3918582001389977415888415214193}{309485009821345068724781056}\cdot t^{51}+\frac{23023926505862770531141610129475}{19807040628566084398385987584}\cdot t^{49}-\frac{483986443066184365519493306025}{4951760157141521099596496896}\cdot t^{47}+\frac{9512533544628096347755859342055}{1267650600228229401496703205376}\cdot t^{45}-\frac{664601849624687041939188479085}{1267650600228229401496703205376}\cdot t^{43}+\frac{673552716286298988631972162305}{20282409603651670423947251286016}\cdot t^{41}-\frac{19260469638539725578121675725}{10141204801825835211973625643008}\cdot t^{39}+\frac{15840186461884502389997959725}{162259276829213363391578010288128}\cdot t^{37}-\frac{728058259738790793080651565}{162259276829213363391578010288128}\cdot t^{35}+\frac{952076185812264883259313585}{5192296858534827628530496329220096}\cdot t^{33}-\frac{4296255180063549999665985}{649037107316853453566312041152512}\cdot t^{31}+\frac{4352415378495753267635475}{20769187434139310514121985316880384}\cdot t^{29}-\frac{119834575048777690672725}{20769187434139310514121985316880384}\cdot t^{27}+\frac{45472363072563210190407}{332306998946228968225951765070086144}\cdot t^{25}-\frac{459316798712759698893}{166153499473114484112975882535043072}\cdot t^{23}+\frac{124819710069095815059}{2658455991569831745807614120560689152}\cdot t^{21}-\frac{1754728820090381655}{2658455991569831745807614120560689152}\cdot t^{19}+\frac{2564603660132096265}{340282366920938463463374607431768211456}\cdot t^{17}-\frac{5809228810425801}{85070591730234615865843651857942052864}\cdot t^{15}+\frac{2595612872743443}{5444517870735015415413993718908291383296}\cdot t^{13}-\frac{13438059476569}{5444517870735015415413993718908291383296}\cdot t^{11}+\frac{783768050065}{87112285931760246646623899502532662132736}\cdot t^9-\frac{933921945}{43556142965880123323311949751266331066368}\cdot t^7+\frac{20753821}{696898287454081973172991196020261297061888}\cdot t^5-\frac{13717}{696898287454081973172991196020261297061888}\cdot t^3+\frac{87}{22300745198530623141535718272648361505980416}\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.