Rule: Q[6, 91, 98]

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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{97}-1536\cdot t^{95}+17860\cdot t^{93}-134044\cdot t^{91}+\frac{2919735}{4}\cdot t^{89}-\frac{6147141}{2}\cdot t^{87}+\frac{333281949}{32}\cdot t^{85}-\frac{933921945}{32}\cdot t^{83}+\frac{70625252863}{1024}\cdot t^{81}-\frac{35709397515}{256}\cdot t^{79}+\frac{2000375522613}{8192}\cdot t^{77}-\frac{3058045339167}{8192}\cdot t^{75}+\frac{65783533458825}{131072}\cdot t^{73}-\frac{39112924418505}{65536}\cdot t^{71}+\frac{661194674693775}{1048576}\cdot t^{69}-\frac{622956910374135}{1048576}\cdot t^{67}+\frac{33594090947249085}{67108864}\cdot t^{65}-\frac{1585777713559325}{4194304}\cdot t^{63}+\frac{68822752768474705}{268435456}\cdot t^{61}-\frac{41953909915492575}{268435456}\cdot t^{59}+\frac{368118665976450235}{4294967296}\cdot t^{57}-\frac{90834476020163045}{2147483648}\cdot t^{55}+\frac{645402855932737425}{34359738368}\cdot t^{53}-\frac{257786995789945557}{34359738368}\cdot t^{51}+\frac{2961066843533158425}{1099511627776}\cdot t^{49}-\frac{238507849862670843}{274877906944}\cdot t^{47}+\frac{2203649450440574199}{8796093022208}\cdot t^{45}-\frac{569017463728786765}{8796093022208}\cdot t^{43}+\frac{2097235794886099791}{140737488355328}\cdot t^{41}-\frac{214859239356147155}{70368744177664}\cdot t^{39}+\frac{624355672011392321}{1125899906842624}\cdot t^{37}-\frac{100101318622914609}{1125899906842624}\cdot t^{35}+\frac{1804857108504066435}{144115188075855872}\cdot t^{33}-\frac{27767032438524099}{18014398509481984}\cdot t^{31}+\frac{759510004936100355}{4611686018427387904}\cdot t^{29}-\frac{69923143311577493}{4611686018427387904}\cdot t^{27}+\frac{87967825456500717}{73786976294838206464}\cdot t^{25}-\frac{2923166552608575}{36893488147419103232}\cdot t^{23}+\frac{2594951360736735}{590295810358705651712}\cdot t^{21}-\frac{118413686604675}{590295810358705651712}\cdot t^{19}+\frac{139646485582065}{18889465931478580854784}\cdot t^{17}-\frac{1015828093665}{4722366482869645213696}\cdot t^{15}+\frac{725591495475}{151115727451828646838272}\cdot t^{13}-\frac{11965356585}{151115727451828646838272}\cdot t^{11}+\frac{2215806775}{2417851639229258349412352}\cdot t^9-\frac{8361535}{1208925819614629174706176}\cdot t^7+\frac{587265}{19342813113834066795298816}\cdot t^5-\frac{1225}{19342813113834066795298816}\cdot t^3+\frac{49}{1237940039285380274899124224}\cdot t$
• $P_3$:
  $64\cdot t^{195}-3104\cdot t^{193}+74112\cdot t^{191}-1161280\cdot t^{189}+\frac{53727345}{4}\cdot t^{187}-\frac{978400269}{8}\cdot t^{185}+\frac{14607344367}{16}\cdot t^{183}-\frac{183867048937}{32}\cdot t^{181}+\frac{31863768374295}{1024}\cdot t^{179}-\frac{301617168134815}{2048}\cdot t^{177}+\frac{1262900271738677}{2048}\cdot t^{175}-\frac{9448479920010495}{4096}\cdot t^{173}+\frac{1018655682970406845}{131072}\cdot t^{171}-\frac{6223690774264339425}{262144}\cdot t^{169}+\frac{34674848599472748225}{524288}\cdot t^{167}-\frac{177026915814840428415}{1048576}\cdot t^{165}+\frac{26613046344164344405055}{67108864}\cdot t^{163}-\frac{115468961840947038836655}{134217728}\cdot t^{161}+\frac{116045585870115313687275}{67108864}\cdot t^{159}-\frac{433436992005506528464425}{134217728}\cdot t^{157}+\frac{48253358219085754068866805}{8589934592}\cdot t^{155}-\frac{156708525263888020356986481}{17179869184}\cdot t^{153}+\frac{476020567337641039893165831}{34359738368}\cdot t^{151}-\frac{1354846173686550584767555425}{68719476736}\cdot t^{149}+\frac{57901294228945374990880101225}{2199023255552}\cdot t^{147}-\frac{145342406636447443047282892689}{4398046511104}\cdot t^{145}+\frac{171648724579695849028691561049}{4398046511104}\cdot t^{143}-\frac{381930637882457145559567262619}{8796093022208}\cdot t^{141}+\frac{12821957128911061315214043816495}{281474976710656}\cdot t^{139}-\frac{25392399509268219920342327946315}{562949953421312}\cdot t^{137}+\frac{47501123258703360798776933162223}{1125899906842624}\cdot t^{135}-\frac{83997587463337614550329884741409}{2251799813685248}\cdot t^{133}+\frac{8991839301868019274668240588537661}{288230376151711744}\cdot t^{131}-\frac{14234153496078487474214550773637885}{576460752303423488}\cdot t^{129}+\frac{1333482789392973772094173601887645}{72057594037927936}\cdot t^{127}-\frac{1893379910902073318638062642183327}{144115188075855872}\cdot t^{125}+\frac{163041047883234091327166505299119825}{18446744073709551616}\cdot t^{123}-\frac{207937613848020633559022656681845325}{36893488147419103232}\cdot t^{121}+\frac{251436888163995636182295883995702375}{73786976294838206464}\cdot t^{119}-\frac{288312655854877243448619859796476625}{147573952589676412928}\cdot t^{117}+\frac{5016640211874864036005985560458693275}{4722366482869645213696}\cdot t^{115}-\frac{5174520312956685091427102336554954275}{9444732965739290427392}\cdot t^{113}+\frac{2531258854390066733035768675457618325}{9444732965739290427392}\cdot t^{111}-\frac{2348888175414403010363788989765733375}{18889465931478580854784}\cdot t^{109}+\frac{33075492345667885452156129171677288625}{604462909807314587353088}\cdot t^{107}-\frac{27604285076126943105103371380806755525}{1208925819614629174706176}\cdot t^{105}+\frac{21843390799370015848386146049160128285}{2417851639229258349412352}\cdot t^{103}-\frac{16384882460244280058770873225223212035}{4835703278458516698824704}\cdot t^{101}+\frac{372719173082133397733301395438636129625}{309485009821345068724781056}\cdot t^{99}-\frac{251014953300212288269366245907652903625}{618970019642690137449562112}\cdot t^{97}+\frac{40024850087869466239115384963905202715}{309485009821345068724781056}\cdot t^{95}-\frac{24166457828578386309350938994433634905}{618970019642690137449562112}\cdot t^{93}+\frac{441812421327599729194031269308491838135}{39614081257132168796771975168}\cdot t^{91}-\frac{238715116154706543218044339334776893675}{79228162514264337593543950336}\cdot t^{89}+\frac{121910327968418208560493170687922054725}{158456325028528675187087900672}\cdot t^{87}-\frac{58809353569291104864578330308641702995}{316912650057057350374175801344}\cdot t^{85}+\frac{428468147433406621156213549391532407535}{10141204801825835211973625643008}\cdot t^{83}-\frac{184030935973227657679489424281128964135}{20282409603651670423947251286016}\cdot t^{81}+\frac{37247640714221489935129043894981124675}{20282409603651670423947251286016}\cdot t^{79}-\frac{14197696528580528329844436996218835225}{40564819207303340847894502572032}\cdot t^{77}+\frac{81455804005150246849264358139090807585}{1298074214633706907132624082305024}\cdot t^{75}-\frac{27448677123775584093103654382025135525}{2596148429267413814265248164610048}\cdot t^{73}+\frac{8682609952007972435806018742893844025}{5192296858534827628530496329220096}\cdot t^{71}-\frac{2575043051765104607110389852737940375}{10384593717069655257060992658440192}\cdot t^{69}+\frac{91531075749105081943651130220048607875}{2658455991569831745807614120560689152}\cdot t^{67}-\frac{23766906456990174536396083255023778275}{5316911983139663491615228241121378304}\cdot t^{65}+\frac{720209286575459834436244947121932675}{1329227995784915872903807060280344576}\cdot t^{63}-\frac{162740800264014006323497209502387425}{2658455991569831745807614120560689152}\cdot t^{61}+\frac{8759284249504283281529408629099087875}{1361129467683753853853498429727072845824}\cdot t^{59}-\frac{1710274489433051317436587717036236375}{2722258935367507707706996859454145691648}\cdot t^{57}+\frac{309478240945028333631382539273223725}{5444517870735015415413993718908291383296}\cdot t^{55}-\frac{51783119752492064838603162909378843}{10889035741470030830827987437816582766592}\cdot t^{53}+\frac{127880177453286855461640068976924813}{348449143727040986586495598010130648530944}\cdot t^{51}-\frac{18158728839841935707048790282389925}{696898287454081973172991196020261297061888}\cdot t^{49}+\frac{1182690801708801306573403709132175}{696898287454081973172991196020261297061888}\cdot t^{47}-\frac{140880303762778425609459990035469}{1393796574908163946345982392040522594123776}\cdot t^{45}+\frac{244686843377457265532219982693183}{44601490397061246283071436545296723011960832}\cdot t^{43}-\frac{24113523908091663295383023504523}{89202980794122492566142873090593446023921664}\cdot t^{41}+\frac{2148314820147236408323998182715}{178405961588244985132285746181186892047843328}\cdot t^{39}-\frac{172227770391550598135679179205}{356811923176489970264571492362373784095686656}\cdot t^{37}+\frac{395529983037147235718490804657}{22835963083295358096932575511191922182123945984}\cdot t^{35}-\frac{25264663436081868518787120641}{45671926166590716193865151022383844364247891968}\cdot t^{33}+\frac{356753912447882610663232769}{22835963083295358096932575511191922182123945984}\cdot t^{31}-\frac{17687447413185351738821115}{45671926166590716193865151022383844364247891968}\cdot t^{29}+\frac{24425522618208342877419635}{2923003274661805836407369665432566039311865085952}\cdot t^{27}-\frac{908676040168641054581271}{5846006549323611672814739330865132078623730171904}\cdot t^{25}+\frac{28816364910210604267905}{11692013098647223345629478661730264157247460343808}\cdot t^{23}-\frac{768801046323239784855}{23384026197294446691258957323460528314494920687616}\cdot t^{21}+\frac{271798349710236287575}{748288838313422294120286634350736906063837462003712}\cdot t^{19}-\frac{4880554216155665775}{1496577676626844588240573268701473812127674924007424}\cdot t^{17}+\frac{34788017473646255}{1496577676626844588240573268701473812127674924007424}\cdot t^{15}-\frac{382285906303805}{2993155353253689176481146537402947624255349848014848}\cdot t^{13}+\frac{49863379083105}{95780971304118053647396689196894323976171195136475136}\cdot t^{11}-\frac{286301894725}{191561942608236107294793378393788647952342390272950272}\cdot t^9+\frac{1074975825}{383123885216472214589586756787577295904684780545900544}\cdot t^7-\frac{2352735}{766247770432944429179173513575154591809369561091801088}\cdot t^5+\frac{156849}{98079714615416886934934209737619787751599303819750539264}\cdot t^3-\frac{49}{196159429230833773869868419475239575503198607639501078528}\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.