Rule: Q[11, 12, 22, 44, 88]

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.

• $P_1$:
  $1024\cdot t^{11}-2816\cdot t^9+2816\cdot t^7-1232\cdot t^5+220\cdot t^3-11\cdot t$
• $P_2$:
  $1024\cdot t^{23}-6144\cdot t^{21}+16064\cdot t^{19}-24000\cdot t^{17}+22576\cdot t^{15}-13888\cdot t^{13}+\frac{22477}{4}\cdot t^{11}-\frac{5863}{4}\cdot t^9+\frac{15015}{64}\cdot t^7-\frac{671}{32}\cdot t^5+\frac{891}{1024}\cdot t^3-\frac{11}{1024}\cdot t$
• $P_3$:
  $1024\cdot t^{45}-11776\cdot t^{43}+63232\cdot t^{41}-210560\cdot t^{39}+487084\cdot t^{37}-830946\cdot t^{35}+1083138\cdot t^{33}-1102926\cdot t^{31}+\frac{14231635}{16}\cdot t^{29}-\frac{18324317}{32}\cdot t^{27}+\frac{18897879}{64}\cdot t^{25}-\frac{15602145}{128}\cdot t^{23}+\frac{657218445}{16384}\cdot t^{21}-\frac{342120975}{32768}\cdot t^{19}+\frac{34787385}{16384}\cdot t^{17}-\frac{21729825}{65536}\cdot t^{15}+\frac{162806535}{4194304}\cdot t^{13}-\frac{27638065}{8388608}\cdot t^{11}+\frac{3244725}{16777216}\cdot t^9-\frac{245663}{33554432}\cdot t^7+\frac{171787}{1073741824}\cdot t^5-\frac{3553}{2147483648}\cdot t^3+\frac{11}{2147483648}\cdot t$
• $P_4$:
  $1024\cdot t^{89}-23040\cdot t^{87}+250496\cdot t^{85}-1753024\cdot t^{83}+8875024\cdot t^{81}-34635816\cdot t^{79}+108420390\cdot t^{77}-279679829\cdot t^{75}+\frac{38795649035}{64}\cdot t^{73}-\frac{143359883095}{128}\cdot t^{71}+\frac{913225967115}{512}\cdot t^{69}-\frac{2528783497225}{1024}\cdot t^{67}+\frac{1532266590535}{512}\cdot t^{65}-\frac{6535996177987}{2048}\cdot t^{63}+\frac{24636158350593}{8192}\cdot t^{61}-\frac{41162206085151}{16384}\cdot t^{59}+\frac{1955846684508275}{1048576}\cdot t^{57}-\frac{2585526856530247}{2097152}\cdot t^{55}+\frac{6092893079963943}{8388608}\cdot t^{53}-\frac{6402633666964821}{16777216}\cdot t^{51}+\frac{12001857566635365}{67108864}\cdot t^{49}-\frac{10028828543759025}{134217728}\cdot t^{47}+\frac{14928898487394255}{536870912}\cdot t^{45}-\frac{9883487638698345}{1073741824}\cdot t^{43}+\frac{743541401286540045}{274877906944}\cdot t^{41}-\frac{387014154516853521}{549755813888}\cdot t^{39}+\frac{355711892958199365}{2199023255552}\cdot t^{37}-\frac{143802805044275447}{4398046511104}\cdot t^{35}+\frac{50917064167129671}{8796093022208}\cdot t^{33}-\frac{15708530226305917}{17592186044416}\cdot t^{31}+\frac{8393778564455207}{70368744177664}\cdot t^{29}-\frac{1928125147271785}{140737488355328}\cdot t^{27}+\frac{24164204479438023}{18014398509481984}\cdot t^{25}-\frac{3993055042243995}{36028797018963968}\cdot t^{23}+\frac{1100199079479955}{144115188075855872}\cdot t^{21}-\frac{124518754992905}{288230376151711744}\cdot t^{19}+\frac{22742757165275}{1152921504606846976}\cdot t^{17}-\frac{1638695180535}{2305843009213693952}\cdot t^{15}+\frac{181072248833}{9223372036854775808}\cdot t^{13}-\frac{7388798231}{18446744073709551616}\cdot t^{11}+\frac{6771318059}{1180591620717411303424}\cdot t^9-\frac{126468375}{2361183241434822606848}\cdot t^7+\frac{2748603}{9444732965739290427392}\cdot t^5-\frac{14201}{18889465931478580854784}\cdot t^3+\frac{11}{18889465931478580854784}\cdot t$
• $P_5$:
  $1024\cdot t^{177}-45568\cdot t^{175}+996736\cdot t^{173}-14285632\cdot t^{171}+150892680\cdot t^{169}-1252593524\cdot t^{167}+8510335197\cdot t^{165}-\frac{97326660959}{2}\cdot t^{163}+\frac{3824170739829}{16}\cdot t^{161}-\frac{32769231701085}{32}\cdot t^{159}+\frac{495889009554411}{128}\cdot t^{157}-\frac{3345601480915941}{256}\cdot t^{155}+\frac{81152821787667903}{2048}\cdot t^{153}-\frac{445297018294859787}{4096}\cdot t^{151}+\frac{4446794263784286775}{16384}\cdot t^{149}-\frac{20301119215922726805}{32768}\cdot t^{147}+\frac{5445932761972879502795}{4194304}\cdot t^{145}-\frac{21032883492456638582115}{8388608}\cdot t^{143}+\frac{150163952971303045519745}{33554432}\cdot t^{141}-\frac{496822980814169305871575}{67108864}\cdot t^{139}+\frac{6108619120671886773126095}{536870912}\cdot t^{137}-\frac{17482100604600809317442995}{1073741824}\cdot t^{135}+\frac{93338509084071455234525355}{4294967296}\cdot t^{133}-\frac{232814082566548526010051945}{8589934592}\cdot t^{131}+\frac{543389378110796077984694025}{17179869184}\cdot t^{129}-\frac{1188326950918297969996955283}{34359738368}\cdot t^{127}+\frac{4875483353476255859580460317}{137438953472}\cdot t^{125}-\frac{9391639593875694552061633955}{274877906944}\cdot t^{123}+\frac{68012490385920451725072978805}{2199023255552}\cdot t^{121}-\frac{115819592394014202432054286025}{4398046511104}\cdot t^{119}+\frac{371286326145287474970495843605}{17592186044416}\cdot t^{117}-\frac{560486526953626718139061908255}{35184372088832}\cdot t^{115}+\frac{51024344983122318401566871956915}{4503599627370496}\cdot t^{113}-\frac{68417309370402751372170334905435}{9007199254740992}\cdot t^{111}+\frac{173016073183708901663386261355425}{36028797018963968}\cdot t^{109}-\frac{206343887102222678892759875748615}{72057594037927936}\cdot t^{107}+\frac{928651498166099951612533008358635}{576460752303423488}\cdot t^{105}-\frac{985827512546780209917405213170895}{1152921504606846976}\cdot t^{103}+\frac{1974911770333073949231366364673535}{4611686018427387904}\cdot t^{101}-\frac{1866491217441766154017427789947125}{9223372036854775808}\cdot t^{99}+\frac{6657180981892573244405214486081825}{73786976294838206464}\cdot t^{97}-\frac{5599609675555337390909824299260825}{147573952589676412928}\cdot t^{95}+\frac{8884380876568970592590994304718175}{590295810358705651712}\cdot t^{93}-\frac{6645381127442468969392710741767825}{1180591620717411303424}\cdot t^{91}+\frac{18740415826437066307843305498364875}{9444732965739290427392}\cdot t^{89}-\frac{12448302537001431009432384776489575}{18889465931478580854784}\cdot t^{87}+\frac{15573946933041332340166579000820275}{75557863725914323419136}\cdot t^{85}-\frac{9169620723823122869669873230992425}{151115727451828646838272}\cdot t^{83}+\frac{1300092079470091208074558333278285325}{77371252455336267181195264}\cdot t^{81}-\frac{676848315336369800157873997743727125}{154742504910672534362390528}\cdot t^{79}+\frac{661979477309762374617298456119219255}{618970019642690137449562112}\cdot t^{77}-\frac{303816030624858108662474758469058321}{1237940039285380274899124224}\cdot t^{75}+\frac{522974677235201565907929512855052897}{9903520314283042199192993792}\cdot t^{73}-\frac{210812842359804438103760004679330653}{19807040628566084398385987584}\cdot t^{71}+\frac{159027372581312504755614581111263605}{79228162514264337593543950336}\cdot t^{69}-\frac{56056225488844534296515840495334423}{158456325028528675187087900672}\cdot t^{67}+\frac{36884621793257125482743388415427601}{633825300114114700748351602688}\cdot t^{65}-\frac{11309902702365746529402691663432797}{1267650600228229401496703205376}\cdot t^{63}+\frac{6454359051628831623532914912060291}{5070602400912917605986812821504}\cdot t^{61}-\frac{1710954066002447872550628615473565}{10141204801825835211973625643008}\cdot t^{59}+\frac{1682329739422939238941416577800243}{81129638414606681695789005144064}\cdot t^{57}-\frac{382726331725414163866007864178783}{162259276829213363391578010288128}\cdot t^{55}+\frac{160812668480751542399000297779107}{649037107316853453566312041152512}\cdot t^{53}-\frac{31125940905050035664453141432553}{1298074214633706907132624082305024}\cdot t^{51}+\frac{708625293569331937458469556207175}{332306998946228968225951765070086144}\cdot t^{49}-\frac{115494057206147472208813241073135}{664613997892457936451903530140172288}\cdot t^{47}+\frac{34391467430578502180348106852045}{2658455991569831745807614120560689152}\cdot t^{45}-\frac{4661831789158422131811340625115}{5316911983139663491615228241121378304}\cdot t^{43}+\frac{2292681194944671798881612004615}{42535295865117307932921825928971026432}\cdot t^{41}-\frac{254622423431232331236089365275}{85070591730234615865843651857942052864}\cdot t^{39}+\frac{50852573763557162331119743995}{340282366920938463463374607431768211456}\cdot t^{37}-\frac{4542673367102596075137023145}{680564733841876926926749214863536422912}\cdot t^{35}+\frac{1443758723086204494332198535}{5444517870735015415413993718908291383296}\cdot t^{33}-\frac{101377236006887695045390815}{10889035741470030830827987437816582766592}\cdot t^{31}+\frac{12490030210559268262659225}{43556142965880123323311949751266331066368}\cdot t^{29}-\frac{669389458677874948871319}{87112285931760246646623899502532662132736}\cdot t^{27}+\frac{123652917127145571570405}{696898287454081973172991196020261297061888}\cdot t^{25}-\frac{4865995258543446734889}{1393796574908163946345982392040522594123776}\cdot t^{23}+\frac{322087223884589900397}{5575186299632655785383929568162090376495104}\cdot t^{21}-\frac{8826041066193003735}{11150372599265311570767859136324180752990208}\cdot t^{19}+\frac{12576296935888279659}{1427247692705959881058285969449495136382746624}\cdot t^{17}-\frac{222256791154438979}{2854495385411919762116571938898990272765493248}\cdot t^{15}+\frac{6054866885017601}{11417981541647679048466287755595961091061972992}\cdot t^{13}-\frac{61180092703639}{22835963083295358096932575511191922182123945984}\cdot t^{11}+\frac{1741556889215}{182687704666362864775460604089535377456991567872}\cdot t^9-\frac{8104977507}{365375409332725729550921208179070754913983135744}\cdot t^7+\frac{43977659}{1461501637330902918203684832716283019655932542976}\cdot t^5-\frac{56793}{2923003274661805836407369665432566039311865085952}\cdot t^3+\frac{11}{2923003274661805836407369665432566039311865085952}\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.