Rule: Q[7, 92, 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.

• $P_1$:
  $64\cdot t^7-112\cdot t^5+56\cdot t^3-7\cdot t$
• $P_2$:
  $64\cdot t^{99}-1600\cdot t^{97}+19396\cdot t^{95}-151904\cdot t^{93}+\frac{3455911}{4}\cdot t^{91}-\frac{15214017}{4}\cdot t^{89}+\frac{431636205}{32}\cdot t^{87}-\frac{633601947}{16}\cdot t^{85}+\frac{100510755103}{1024}\cdot t^{83}-\frac{213462842923}{1024}\cdot t^{81}+\frac{3143076243093}{8192}\cdot t^{79}-\frac{1264605215445}{2048}\cdot t^{77}+\frac{114712258885497}{131072}\cdot t^{75}-\frac{144009382295835}{131072}\cdot t^{73}+\frac{1287001465389855}{1048576}\cdot t^{71}-\frac{642075792533955}{524288}\cdot t^{69}+\frac{73463333211193725}{67108864}\cdot t^{67}-\frac{58966534364198285}{67108864}\cdot t^{65}+\frac{170312526436271505}{268435456}\cdot t^{63}-\frac{6923541417747955}{16777216}\cdot t^{61}+\frac{1039381224624331435}{4294967296}\cdot t^{59}-\frac{549787618016776325}{4294967296}\cdot t^{57}+\frac{2098754472255346145}{34359738368}\cdot t^{55}-\frac{451594925861341491}{17179869184}\cdot t^{53}+\frac{11210250708811416249}{1099511627776}\cdot t^{51}-\frac{3915098242983841797}{1099511627776}\cdot t^{49}+\frac{9835900646046041175}{8796093022208}\cdot t^{47}-\frac{693166728542340241}{2199023255552}\cdot t^{45}+\frac{11201515214546688031}{140737488355328}\cdot t^{43}-\frac{2526954273598394101}{140737488355328}\cdot t^{41}+\frac{4062103501709746801}{1125899906842624}\cdot t^{39}-\frac{362228495317153465}{562949953421312}\cdot t^{37}+\frac{14617825892237136387}{144115188075855872}\cdot t^{35}-\frac{2026993368012259227}{144115188075855872}\cdot t^{33}+\frac{7867870309198269699}{4611686018427387904}\cdot t^{31}-\frac{103679143530959731}{576460752303423488}\cdot t^{29}+\frac{1206738118441740605}{73786976294838206464}\cdot t^{27}-\frac{93814158561717867}{73786976294838206464}\cdot t^{25}+\frac{49365616202473935}{590295810358705651712}\cdot t^{23}-\frac{1356682523670705}{295147905179352825856}\cdot t^{21}+\frac{3928884456931665}{18889465931478580854784}\cdot t^{19}-\frac{143709797956725}{18889465931478580854784}\cdot t^{17}+\frac{33232090492755}{151115727451828646838272}\cdot t^{15}-\frac{184389213015}{37778931862957161709568}\cdot t^{13}+\frac{193661512135}{2417851639229258349412352}\cdot t^{11}-\frac{2232529845}{2417851639229258349412352}\cdot t^9+\frac{134371825}{19342813113834066795298816}\cdot t^7-\frac{294245}{9671406556917033397649408}\cdot t^5+\frac{78449}{1237940039285380274899124224}\cdot t^3-\frac{49}{1237940039285380274899124224}\cdot t$
• $P_3$:
  $64\cdot t^{197}-3168\cdot t^{195}+77216\cdot t^{193}-1235392\cdot t^{191}+\frac{58372465}{4}\cdot t^{189}-\frac{1085854959}{8}\cdot t^{187}+\frac{16564144905}{16}\cdot t^{185}-\frac{213081737671}{32}\cdot t^{183}+\frac{37747513940279}{1024}\cdot t^{181}-\frac{365344704883405}{2048}\cdot t^{179}+\frac{391129359968373}{512}\cdot t^{177}-\frac{11974280463487849}{4096}\cdot t^{175}+\frac{1321007040410742685}{131072}\cdot t^{173}-\frac{8261002140205153115}{262144}\cdot t^{171}+\frac{47122230148001427075}{524288}\cdot t^{169}-\frac{246376613013785924865}{1048576}\cdot t^{167}+\frac{37942768956314131823615}{67108864}\cdot t^{165}-\frac{168695054529275727646765}{134217728}\cdot t^{163}+\frac{347560133581177666211205}{134217728}\cdot t^{161}-\frac{665528163745737155838975}{134217728}\cdot t^{159}+\frac{75993325707438171890590005}{8589934592}\cdot t^{157}-\frac{253215241702059528494720091}{17179869184}\cdot t^{155}+\frac{789437617865417080607138793}{34359738368}\cdot t^{153}-\frac{2306887308361832664553887087}{68719476736}\cdot t^{151}+\frac{101256371786914993703441874825}{2199023255552}\cdot t^{149}-\frac{261144995094338193029043095139}{4398046511104}\cdot t^{147}+\frac{158495565608071646037987226869}{2199023255552}\cdot t^{145}-\frac{725228087041848843616950384717}{8796093022208}\cdot t^{143}+\frac{25043737541149689973120196220303}{281474976710656}\cdot t^{141}-\frac{51036313767090342550770415579305}{562949953421312}\cdot t^{139}+\frac{98285922277239800639461589054853}{1125899906842624}\cdot t^{137}-\frac{178999833980744336147883751065855}{2251799813685248}\cdot t^{135}+\frac{19743530497175233937110465835438013}{288230376151711744}\cdot t^{133}-\frac{32217832099814526023551031950713207}{576460752303423488}\cdot t^{131}+\frac{24902015811222277650967939588739045}{576460752303423488}\cdot t^{129}-\frac{4560345489688020862826409845958617}{144115188075855872}\cdot t^{127}+\frac{405393676478699476112838523498585681}{18446744073709551616}\cdot t^{125}-\frac{534019709614488816213355667280084975}{36893488147419103232}\cdot t^{123}+\frac{667312115860036903300341197359393025}{73786976294838206464}\cdot t^{121}-\frac{791186432182868515813211627787881375}{147573952589676412928}\cdot t^{119}+\frac{14242645199230935826361821073945945275}{4722366482869645213696}\cdot t^{117}-\frac{15207800736706413163439073457472340825}{9444732965739290427392}\cdot t^{115}+\frac{963222395918343978057858876501571575}{1180591620717411303424}\cdot t^{113}-\frac{7411405884194536476435326340680970025}{18889465931478580854784}\cdot t^{111}+\frac{108239913958928781783797376844180756625}{604462909807314587353088}\cdot t^{109}-\frac{93755269767462714009415629724161332775}{1208925819614629174706176}\cdot t^{107}+\frac{77051960951623902058592888810773639335}{2417851639229258349412352}\cdot t^{105}-\frac{60071664058984311755543165323543468605}{4835703278458516698824704}\cdot t^{103}+\frac{1421351650537767321494637281852921699865}{309485009821345068724781056}\cdot t^{101}-\frac{996453299464479083735969036784925162875}{618970019642690137449562112}\cdot t^{99}+\frac{331064653475951220747597015835463309055}{618970019642690137449562112}\cdot t^{97}-\frac{104216158004317318787581708922244040335}{618970019642690137449562112}\cdot t^{95}+\frac{1988465722356616452992491364952244472055}{39614081257132168796771975168}\cdot t^{93}-\frac{1122339958809906001606106877951760569945}{79228162514264337593543950336}\cdot t^{91}+\frac{599340560277831294996581849357475842075}{158456325028528675187087900672}\cdot t^{89}-\frac{302630009506127521985564671684485812445}{316912650057057350374175801344}\cdot t^{87}+\frac{2310367461650721976822720119268066903375}{10141204801825835211973625643008}\cdot t^{85}-\frac{1040967230840040899991916523064193779205}{20282409603651670423947251286016}\cdot t^{83}+\frac{110639288343724573807309234088055044405}{10141204801825835211973625643008}\cdot t^{81}-\frac{88692977957023508200102524786181084575}{40564819207303340847894502572032}\cdot t^{79}+\frac{535782092919727153404286342018093534785}{1298074214633706907132624082305024}\cdot t^{77}-\frac{190360285134076077791632370660206750695}{2596148429267413814265248164610048}\cdot t^{75}+\frac{63579964199559140622013327506944115075}{5192296858534827628530496329220096}\cdot t^{73}-\frac{19940262955781049478722427338525628425}{10384593717069655257060992658440192}\cdot t^{71}+\frac{750742097000971861363910932520961343875}{2658455991569831745807614120560689152}\cdot t^{69}-\frac{206829057955200338423698343695120994025}{5316911983139663491615228241121378304}\cdot t^{67}+\frac{26647743603292013874141063043511508975}{5316911983139663491615228241121378304}\cdot t^{65}-\frac{1603159373414933675195987103746252775}{2658455991569831745807614120560689152}\cdot t^{63}+\frac{92082573984679454519159979894321449475}{1361129467683753853853498429727072845824}\cdot t^{61}-\frac{19228842988441617880495404975234412125}{2722258935367507707706996859454145691648}\cdot t^{59}+\frac{3730027219811130968504557973345696475}{5444517870735015415413993718908291383296}\cdot t^{57}-\frac{670739601642548732101368241455826293}{10889035741470030830827987437816582766592}\cdot t^{55}+\frac{1784940009533032930296941282077047789}{348449143727040986586495598010130648530944}\cdot t^{53}-\frac{273919083746415646630328928236239551}{696898287454081973172991196020261297061888}\cdot t^{51}+\frac{4835354910387684253405548497880525}{174224571863520493293247799005065324265472}\cdot t^{49}-\frac{2506261907180381038756267408299819}{1393796574908163946345982392040522594123776}\cdot t^{47}+\frac{4752856563786366885034939663828191}{44601490397061246283071436545296723011960832}\cdot t^{45}-\frac{513487210663006194359822988890889}{89202980794122492566142873090593446023921664}\cdot t^{43}+\frac{50375362636330562999090045191761}{178405961588244985132285746181186892047843328}\cdot t^{41}-\frac{4468857410686023414783675544635}{356811923176489970264571492362373784095686656}\cdot t^{39}+\frac{11418107288096385516401958273777}{22835963083295358096932575511191922182123945984}\cdot t^{37}-\frac{816324629510376339955768729955}{45671926166590716193865151022383844364247891968}\cdot t^{35}+\frac{25978171260977633740113586179}{45671926166590716193865151022383844364247891968}\cdot t^{33}-\frac{731195272308950573065286653}{45671926166590716193865151022383844364247891968}\cdot t^{31}+\frac{1156422157062070854161970995}{2923003274661805836407369665432566039311865085952}\cdot t^{29}-\frac{49759721276585326809420541}{5846006549323611672814739330865132078623730171904}\cdot t^{27}+\frac{1846168445247492713430447}{11692013098647223345629478661730264157247460343808}\cdot t^{25}-\frac{58401530866744448320665}{23384026197294446691258957323460528314494920687616}\cdot t^{23}+\frac{24873431832053909402935}{748288838313422294120286634350736906063837462003712}\cdot t^{21}-\frac{548477253636628240925}{1496577676626844588240573268701473812127674924007424}\cdot t^{19}+\frac{2457671116814656015}{748288838313422294120286634350736906063837462003712}\cdot t^{17}-\frac{69958320853596315}{2993155353253689176481146537402947624255349848014848}\cdot t^{15}+\frac{12283012380804865}{95780971304118053647396689196894323976171195136475136}\cdot t^{13}-\frac{100013060060935}{191561942608236107294793378393788647952342390272950272}\cdot t^{11}+\frac{573678765275}{383123885216472214589586756787577295904684780545900544}\cdot t^9-\frac{2152304385}{766247770432944429179173513575154591809369561091801088}\cdot t^7+\frac{301306929}{98079714615416886934934209737619787751599303819750539264}\cdot t^5-\frac{313747}{196159429230833773869868419475239575503198607639501078528}\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 T (first kind) type can be downloaded here packed into a single file.