Rule: Q[22, 23, 46, 92]

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.

• $P_1$:
  $4194304\cdot t^{22}-22020096\cdot t^{20}+49807360\cdot t^{18}-63504384\cdot t^{16}+50135040\cdot t^{14}-25346048\cdot t^{12}+8200192\cdot t^{10}-1647360\cdot t^8+192192\cdot t^6-11440\cdot t^4+264\cdot t^2-1$
• $P_2$:
  $4194304\cdot t^{45}-46137344\cdot t^{43}+236716032\cdot t^{41}-752353280\cdot t^{39}+1659207680\cdot t^{37}-2695200768\cdot t^{35}+3340925952\cdot t^{33}-3230785536\cdot t^{31}+2470913280\cdot t^{29}-1506292480\cdot t^{27}+734317584\cdot t^{25}-286097760\cdot t^{23}+88704330\cdot t^{21}-21710850\cdot t^{19}+\frac{265182525}{64}\cdot t^{17}-\frac{9694845}{16}\cdot t^{15}+\frac{67863915}{1024}\cdot t^{13}-\frac{5368545}{1024}\cdot t^{11}+\frac{4686825}{16384}\cdot t^9-\frac{82225}{8192}\cdot t^7+\frac{26565}{131072}\cdot t^5-\frac{253}{131072}\cdot t^3+\frac{23}{4194304}\cdot t$
• $P_3$:
  $4194304\cdot t^{91}-94371840\cdot t^{89}+1026555904\cdot t^{87}-7191658496\cdot t^{85}+36469063680\cdot t^{83}-142648532992\cdot t^{81}+447850045440\cdot t^{79}-1159517638656\cdot t^{77}+2524366525824\cdot t^{75}-4688833406400\cdot t^{73}+7513569629280\cdot t^{71}-10477677064400\cdot t^{69}+\frac{51209646652255}{4}\cdot t^{67}-\frac{110247837145215}{8}\cdot t^{65}+\frac{26249485034575}{2}\cdot t^{63}-\frac{44385492876645}{4}\cdot t^{61}+\frac{2137511893796325}{256}\cdot t^{59}-\frac{2868457137478833}{512}\cdot t^{57}+\frac{3436980173735899}{1024}\cdot t^{55}-\frac{3679823762074845}{2048}\cdot t^{53}+\frac{56342190490434849}{65536}\cdot t^{51}-\frac{48179941566267225}{131072}\cdot t^{49}+\frac{18395977688938395}{131072}\cdot t^{47}-\frac{12530593498262385}{262144}\cdot t^{45}+\frac{121620466306664325}{8388608}\cdot t^{43}-\frac{65566137955174857}{16777216}\cdot t^{41}+\frac{31331138183708265}{33554432}\cdot t^{39}-\frac{13228702788676823}{67108864}\cdot t^{37}+\frac{629308289804197437}{17179869184}\cdot t^{35}-\frac{204947144189106445}{34359738368}\cdot t^{33}+\frac{14544636039226909}{17179869184}\cdot t^{31}-\frac{3576549845711535}{34359738368}\cdot t^{29}+\frac{48402641245296107}{4398046511104}\cdot t^{27}-\frac{8725899885515631}{8796093022208}\cdot t^{25}+\frac{1327469556620025}{17592186044416}\cdot t^{23}-\frac{168345763320735}{35184372088832}\cdot t^{21}+\frac{280576272201225}{1125899906842624}\cdot t^{19}-\frac{23576679383985}{2251799813685248}\cdot t^{17}+\frac{781293468865}{2251799813685248}\cdot t^{15}-\frac{39688347475}{4503599627370496}\cdot t^{13}+\frac{23813008485}{144115188075855872}\cdot t^{11}-\frac{626358425}{288230376151711744}\cdot t^9+\frac{10737573}{576460752303423488}\cdot t^7-\frac{107019}{1152921504606846976}\cdot t^5+\frac{16215}{73786976294838206464}\cdot t^3-\frac{23}{147573952589676412928}\cdot t$
• $P_4$:
  $4194304\cdot t^{183}-190840832\cdot t^{181}+4270325760\cdot t^{179}-62643240960\cdot t^{177}+677591056384\cdot t^{175}-5763309404160\cdot t^{173}+40143500615680\cdot t^{171}-235466417049600\cdot t^{169}+1187031696177600\cdot t^{167}-5223316298640544\cdot t^{165}+20307893540404184\cdot t^{163}-70448007991055292\cdot t^{161}+219808707103874070\cdot t^{159}-621011509206424245\cdot t^{157}+\frac{6390678102304093533}{4}\cdot t^{155}-\frac{30087867120709805253}{8}\cdot t^{153}+\frac{4165020462852543041451}{512}\cdot t^{151}-\frac{16614602586053205334425}{1024}\cdot t^{149}+\frac{122618880932946882207075}{4096}\cdot t^{147}-\frac{419720322581005739382495}{8192}\cdot t^{145}+\frac{2671878151064451170215395}{32768}\cdot t^{143}-\frac{7925088772350970707331845}{65536}\cdot t^{141}+\frac{43894851954603861325120825}{262144}\cdot t^{139}-\frac{113690392950744162562580025}{524288}\cdot t^{137}+\frac{17652328345485543640549925215}{67108864}\cdot t^{135}-\frac{40167373555953897416043792093}{134217728}\cdot t^{133}+\frac{171659788254217775812089779451}{536870912}\cdot t^{131}-\frac{344817904454980976890763027135}{1073741824}\cdot t^{129}+\frac{162935932874331670398931979855}{536870912}\cdot t^{127}-\frac{290022335690217507199522752129}{1073741824}\cdot t^{125}+\frac{973018658700946182162901008225}{4294967296}\cdot t^{123}-\frac{1539228124864684630986347515225}{8589934592}\cdot t^{121}+\frac{147036791927863295012643196849125}{1099511627776}\cdot t^{119}-\frac{207173452965187275593772403186375}{2199023255552}\cdot t^{117}+\frac{551325118361474843991897854126565}{8796093022208}\cdot t^{115}-\frac{692988715409293883483583975800505}{17592186044416}\cdot t^{113}+\frac{1646108329996250636142687462036635}{70368744177664}\cdot t^{111}-\frac{1847672615301913979343832865551325}{140737488355328}\cdot t^{109}+\frac{3920476212569237809090771538080425}{562949953421312}\cdot t^{107}-\frac{3931568629793129551786695913784985}{1125899906842624}\cdot t^{105}+\frac{119257581770391596404196442718144545}{72057594037927936}\cdot t^{103}-\frac{106849748770231461011639760122533395}{144115188075855872}\cdot t^{101}+\frac{180949440405656900774239030388596125}{576460752303423488}\cdot t^{99}-\frac{144777459245891740995519303383651625}{1152921504606846976}\cdot t^{97}+\frac{109429196468972718518691213726344475}{2305843009213693952}\cdot t^{95}-\frac{78113726975853427367858716113209925}{4611686018427387904}\cdot t^{93}+\frac{105283718967454619495809573891717725}{18446744073709551616}\cdot t^{91}-\frac{66957109671024486230057494189561125}{36893488147419103232}\cdot t^{89}+\frac{1285313928782999451357378172776085125}{2361183241434822606848}\cdot t^{87}-\frac{726887287615601050268775773901033175}{4722366482869645213696}\cdot t^{85}+\frac{774623169190356940137172988903489085}{18889465931478580854784}\cdot t^{83}-\frac{388624892341852376129559145103725985}{37778931862957161709568}\cdot t^{81}+\frac{366883639623427068374059332790230825}{151115727451828646838272}\cdot t^{79}-\frac{162806926930689730327016679292337775}{302231454903657293676544}\cdot t^{77}+\frac{135718822848774401976310770259082715}{1208925819614629174706176}\cdot t^{75}-\frac{53082414856285971174667003166871675}{2417851639229258349412352}\cdot t^{73}+\frac{4982163794368554723108031582947812925}{1237940039285380274899124224}\cdot t^{71}-\frac{1710274489433051317436587717036236375}{2475880078570760549798248448}\cdot t^{69}+\frac{1098058005530908152902636777276138625}{9903520314283042199192993792}\cdot t^{67}-\frac{329194067827639040822743039262039661}{19807040628566084398385987584}\cdot t^{65}+\frac{46016375072680726136512467853833501}{19807040628566084398385987584}\cdot t^{63}-\frac{11977872919758157822818719141481651}{39614081257132168796771975168}\cdot t^{61}+\frac{5795744961173302172331638294265315}{158456325028528675187087900672}\cdot t^{59}-\frac{1300868375779551359944829217038955}{316912650057057350374175801344}\cdot t^{57}+\frac{34603098795736066174532457173236203}{81129638414606681695789005144064}\cdot t^{55}-\frac{6643258139840731515084770381674953}{162259276829213363391578010288128}\cdot t^{53}+\frac{2350901313996026714891323468399611}{649037107316853453566312041152512}\cdot t^{51}-\frac{382370095081634655120096622299975}{1298074214633706907132624082305024}\cdot t^{49}+\frac{114012989811359623331955787988025}{5192296858534827628530496329220096}\cdot t^{47}-\frac{15532204409083774772759194305615}{10384593717069655257060992658440192}\cdot t^{45}+\frac{3853855229321538101511679790115}{41538374868278621028243970633760768}\cdot t^{43}-\frac{433756858042795575927339754515}{83076749736557242056487941267521536}\cdot t^{41}+\frac{1411431046012271318493724598025}{5316911983139663491615228241121378304}\cdot t^{39}-\frac{129071998654213630384283589675}{10633823966279326983230456482242756608}\cdot t^{37}+\frac{21120872507053139517428223765}{42535295865117307932921825928971026432}\cdot t^{35}-\frac{1537237815498057249280708641}{85070591730234615865843651857942052864}\cdot t^{33}+\frac{98886643102214209018057281}{170141183460469231731687303715884105728}\cdot t^{31}-\frac{5581052195961840902220735}{340282366920938463463374607431768211456}\cdot t^{29}+\frac{548114947160258201814615}{1361129467683753853853498429727072845824}\cdot t^{27}-\frac{23193290711663728612047}{2722258935367507707706996859454145691648}\cdot t^{25}+\frac{26761489282688917629285}{174224571863520493293247799005065324265472}\cdot t^{23}-\frac{811537431202240939735}{348449143727040986586495598010130648530944}\cdot t^{21}+\frac{40751520935550118925}{1393796574908163946345982392040522594123776}\cdot t^{19}-\frac{831266859117150225}{2787593149816327892691964784081045188247552}\cdot t^{17}+\frac{26917212580936293}{11150372599265311570767859136324180752990208}\cdot t^{15}-\frac{335865397623091}{22300745198530623141535718272648361505980416}\cdot t^{13}+\frac{6216777649407}{89202980794122492566142873090593446023921664}\cdot t^{11}-\frac{40516977215}{178405961588244985132285746181186892047843328}\cdot t^9+\frac{11050084695}{22835963083295358096932575511191922182123945984}\cdot t^7-\frac{27445509}{45671926166590716193865151022383844364247891968}\cdot t^5+\frac{64883}{182687704666362864775460604089535377456991567872}\cdot t^3-\frac{23}{365375409332725729550921208179070754913983135744}\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.