Rule: Q[16, 68, 85]

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.

• $P_1$:
  $65536\cdot t^{16}-245760\cdot t^{14}+372736\cdot t^{12}-292864\cdot t^{10}+126720\cdot t^8-29568\cdot t^6+3360\cdot t^4-144\cdot t^2+1$
• $P_2$:
  $65536\cdot t^{84}-1359872\cdot t^{82}+13602816\cdot t^{80}-87367680\cdot t^{78}+404884480\cdot t^{76}-1442400960\cdot t^{74}+4109625520\cdot t^{72}-9619233360\cdot t^{70}+18855883575\cdot t^{68}-\frac{125595622175}{4}\cdot t^{66}+\frac{718406958841}{16}\cdot t^{64}-\frac{111203042769}{2}\cdot t^{62}+\frac{960205268841}{16}\cdot t^{60}-\frac{7263091136105}{128}\cdot t^{58}+\frac{24156719613645}{512}\cdot t^{56}-\frac{17714927716673}{512}\cdot t^{54}+\frac{367392196558827}{16384}\cdot t^{52}-\frac{842840921517309}{65536}\cdot t^{50}+\frac{1712239019666175}{262144}\cdot t^{48}-\frac{385048966145025}{131072}\cdot t^{46}+\frac{1226232861415695}{1048576}\cdot t^{44}-\frac{27619435402363035}{67108864}\cdot t^{42}+\frac{34315056105966195}{268435456}\cdot t^{40}-\frac{9384903142585425}{268435456}\cdot t^{38}+\frac{36052387482172425}{4294967296}\cdot t^{36}-\frac{30284005485024837}{17179869184}\cdot t^{34}+\frac{22150361247847371}{68719476736}\cdot t^{32}-\frac{876961939569947}{17179869184}\cdot t^{30}+\frac{956086325095055}{137438953472}\cdot t^{28}-\frac{890149337157465}{1099511627776}\cdot t^{26}+\frac{350664890395365}{4398046511104}\cdot t^{24}-\frac{28907858348005}{4398046511104}\cdot t^{22}+\frac{125994627894135}{281474976710656}\cdot t^{20}-\frac{27900908274925}{1125899906842624}\cdot t^{18}+\frac{4923689695575}{4503599627370496}\cdot t^{16}-\frac{84406109067}{2251799813685248}\cdot t^{14}+\frac{17417133617}{18014398509481984}\cdot t^{12}-\frac{5178066751}{288230376151711744}\cdot t^{10}+\frac{260932815}{1152921504606846976}\cdot t^8-\frac{2036265}{1152921504606846976}\cdot t^6+\frac{135751}{18446744073709551616}\cdot t^4-\frac{903}{73786976294838206464}\cdot t^2+\frac{1}{295147905179352825856}$
• $P_3$:
  $65536\cdot t^{169}-2752512\cdot t^{167}+56774656\cdot t^{165}-766627840\cdot t^{163}+7621827840\cdot t^{161}-59496450048\cdot t^{159}+379743348096\cdot t^{157}-2037833935488\cdot t^{155}+9383313279340\cdot t^{153}-37649816015240\cdot t^{151}+\frac{2131920831862965}{16}\cdot t^{149}-\frac{6719999740457705}{16}\cdot t^{147}+\frac{304271380653382415}{256}\cdot t^{145}-\frac{194548824964558575}{64}\cdot t^{143}+\frac{7235363442729535575}{1024}\cdot t^{141}-\frac{15357642404245272285}{1024}\cdot t^{139}+\frac{1912924003884628655655}{65536}\cdot t^{137}-\frac{1712879663609111933495}{32768}\cdot t^{135}+\frac{90602319048797762798025}{1048576}\cdot t^{133}-\frac{138603547683922405340025}{1048576}\cdot t^{131}+\frac{3147224556076264750587501}{16777216}\cdot t^{129}-\frac{129751347949452909180501}{524288}\cdot t^{127}+\frac{2550713845070203258853043}{8388608}\cdot t^{125}-\frac{2923400221723465728499125}{8388608}\cdot t^{123}+\frac{100156492527813531328442625}{268435456}\cdot t^{121}-\frac{50147319707029395685827135}{134217728}\cdot t^{119}+\frac{3009267791991909291540105255}{8589934592}\cdot t^{117}-\frac{2644508059629253619838274315}{8589934592}\cdot t^{115}+\frac{34878773301548807802897159225}{137438953472}\cdot t^{113}-\frac{6747153260338739782854402775}{34359738368}\cdot t^{111}+\frac{78459753627367631189192626555}{549755813888}\cdot t^{109}-\frac{53587155935331385144997423985}{549755813888}\cdot t^{107}+\frac{4404242917525569350105512919115}{70368744177664}\cdot t^{105}-\frac{1329748193413493068545460104975}{35184372088832}\cdot t^{103}+\frac{24170128927339374010620421908075}{1125899906842624}\cdot t^{101}-\frac{12916312283922099339008796892675}{1125899906842624}\cdot t^{99}+\frac{103908840612447933488443903360475}{18014398509481984}\cdot t^{97}-\frac{6144578869787106003888879471225}{2251799813685248}\cdot t^{95}+\frac{43756849527271815482238990173875}{36028797018963968}\cdot t^{93}-\frac{18319808404547741890097709920125}{36028797018963968}\cdot t^{91}+\frac{230829585897301547815231144993575}{1152921504606846976}\cdot t^{89}-\frac{42726822573919118039537018519325}{576460752303423488}\cdot t^{87}+\frac{7611478249953877170757523156228325}{295147905179352825856}\cdot t^{85}-\frac{2487912227827810062223435054727625}{295147905179352825856}\cdot t^{83}+\frac{12216977361180429497469479785336375}{4722366482869645213696}\cdot t^{81}-\frac{879622370004990923817802544544219}{1180591620717411303424}\cdot t^{79}+\frac{3801004939670935534758274389538203}{18889465931478580854784}\cdot t^{77}-\frac{961921852056491729346368350094169}{18889465931478580854784}\cdot t^{75}+\frac{14586519887741882781071979079296825}{1208925819614629174706176}\cdot t^{73}-\frac{1616350744855189237167193498920225}{604462909807314587353088}\cdot t^{71}+\frac{10711017602573720678294602252844691}{19342813113834066795298816}\cdot t^{69}-\frac{2070196679489038450426687830381747}{19342813113834066795298816}\cdot t^{67}+\frac{5967672566297606276262590342860551}{309485009821345068724781056}\cdot t^{65}-\frac{62554219772511596187238892482815}{19342813113834066795298816}\cdot t^{63}+\frac{156026042421092142214147582399665}{309485009821345068724781056}\cdot t^{61}-\frac{22571356334434673537698820220663}{309485009821345068724781056}\cdot t^{59}+\frac{96790954105808838152888925808407}{9903520314283042199192993792}\cdot t^{57}-\frac{5995899811864264310355951156273}{4951760157141521099596496896}\cdot t^{55}+\frac{43861631628662229068367425946135}{316912650057057350374175801344}\cdot t^{53}-\frac{4614546372293216648053925252235}{316912650057057350374175801344}\cdot t^{51}+\frac{7131571666271334819719702662545}{5070602400912917605986812821504}\cdot t^{49}-\frac{157668978033070569784749028635}{1267650600228229401496703205376}\cdot t^{47}+\frac{203632216551671787260828793255}{20282409603651670423947251286016}\cdot t^{45}-\frac{14952966502459210012477414725}{20282409603651670423947251286016}\cdot t^{43}+\frac{254764693428691823420134065975}{5192296858534827628530496329220096}\cdot t^{41}-\frac{7652272842913087736428935315}{2596148429267413814265248164610048}\cdot t^{39}+\frac{13217562183213515181104524635}{83076749736557242056487941267521536}\cdot t^{37}-\frac{637798609913070649950413955}{83076749736557242056487941267521536}\cdot t^{35}+\frac{437704928371715151926754675}{1329227995784915872903807060280344576}\cdot t^{33}-\frac{2072644947089481993626475}{166153499473114484112975882535043072}\cdot t^{31}+\frac{1101462743310410430898641}{2658455991569831745807614120560689152}\cdot t^{29}-\frac{31810632649311896069487}{2658455991569831745807614120560689152}\cdot t^{27}+\frac{25318666802513549932857}{85070591730234615865843651857942052864}\cdot t^{25}-\frac{268168339244247457275}{42535295865117307932921825928971026432}\cdot t^{23}+\frac{611230538998149609825}{5444517870735015415413993718908291383296}\cdot t^{21}-\frac{9007607943130625829}{5444517870735015415413993718908291383296}\cdot t^{19}+\frac{1724861095493098563}{87112285931760246646623899502532662132736}\cdot t^{17}-\frac{4094768694788811}{21778071482940061661655974875633165533184}\cdot t^{15}+\frac{479320750226115}{348449143727040986586495598010130648530944}\cdot t^{13}-\frac{2600293400865}{348449143727040986586495598010130648530944}\cdot t^{11}+\frac{635627275767}{22300745198530623141535718272648361505980416}\cdot t^9-\frac{793542167}{11150372599265311570767859136324180752990208}\cdot t^7+\frac{36949857}{356811923176489970264571492362373784095686656}\cdot t^5-\frac{25585}{356811923176489970264571492362373784095686656}\cdot t^3+\frac{85}{5708990770823839524233143877797980545530986496}\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.