Rule: Q[9, 18, 54, 82]

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.

• $P_1$:
  $256\cdot t^9-576\cdot t^7+432\cdot t^5-120\cdot t^3+9\cdot t$
• $P_2$:
  $256\cdot t^{27}-1728\cdot t^{25}+5184\cdot t^{23}-9108\cdot t^{21}+10395\cdot t^{19}-\frac{32319}{4}\cdot t^{17}+\frac{8721}{2}\cdot t^{15}-\frac{26163}{16}\cdot t^{13}+\frac{53703}{128}\cdot t^{11}-\frac{36465}{512}\cdot t^9+\frac{3861}{512}\cdot t^7-\frac{7371}{16384}\cdot t^5+\frac{819}{65536}\cdot t^3-\frac{27}{262144}\cdot t$
• $P_3$:
  $256\cdot t^{81}-5184\cdot t^{79}+50544\cdot t^{77}-316008\cdot t^{75}+1423575\cdot t^{73}-\frac{9845145}{2}\cdot t^{71}+\frac{108734157}{8}\cdot t^{69}-\frac{492452379}{16}\cdot t^{67}+\frac{14915235753}{256}\cdot t^{65}-\frac{11969016345}{128}\cdot t^{63}+\frac{65846447667}{512}\cdot t^{61}-\frac{156492206793}{1024}\cdot t^{59}+\frac{1293517709289}{8192}\cdot t^{57}-\frac{2335355502291}{16384}\cdot t^{55}+\frac{7394462517915}{65536}\cdot t^{53}-\frac{10292494292613}{131072}\cdot t^{51}+\frac{201891234201255}{4194304}\cdot t^{49}-\frac{1745765378093205}{67108864}\cdot t^{47}+\frac{3328346338128315}{268435456}\cdot t^{45}-\frac{2797167126270825}{536870912}\cdot t^{43}+\frac{8281448901713295}{4294967296}\cdot t^{41}-\frac{5389514364607065}{8589934592}\cdot t^{39}+\frac{6153513319220085}{34359738368}\cdot t^{37}-\frac{3072143831034915}{68719476736}\cdot t^{35}+\frac{10689623271729675}{1099511627776}\cdot t^{33}-\frac{2015757531240453}{1099511627776}\cdot t^{31}+\frac{1310947205631903}{4398046511104}\cdot t^{29}-\frac{365051142309021}{8796093022208}\cdot t^{27}+\frac{345371835446001}{70368744177664}\cdot t^{25}-\frac{68707924823475}{140737488355328}\cdot t^{23}+\frac{22723013046195}{562949953421312}\cdot t^{21}-\frac{3078601767549}{1125899906842624}\cdot t^{19}+\frac{10743691882671}{72057594037927936}\cdot t^{17}-\frac{1844876383893}{288230376151711744}\cdot t^{15}+\frac{242443079235}{1152921504606846976}\cdot t^{13}-\frac{11745689553}{2305843009213693952}\cdot t^{11}+\frac{1595093643}{18446744073709551616}\cdot t^9-\frac{35272341}{36893488147419103232}\cdot t^7+\frac{906633}{147573952589676412928}\cdot t^5-\frac{5535}{295147905179352825856}\cdot t^3+\frac{81}{4722366482869645213696}\cdot t$
• $P_4$:
  $256\cdot t^{163}-10496\cdot t^{161}+211216\cdot t^{159}-2780800\cdot t^{157}+26939159\cdot t^{155}-204773569\cdot t^{153}+\frac{10174900197}{8}\cdot t^{151}-\frac{26548850955}{4}\cdot t^{149}+\frac{7602738897975}{256}\cdot t^{147}-\frac{29621934673555}{256}\cdot t^{145}+\frac{813761997580105}{2048}\cdot t^{143}-\frac{621726317784845}{512}\cdot t^{141}+\frac{109083974984801453}{32768}\cdot t^{139}-\frac{270042615017370055}{32768}\cdot t^{137}+\frac{4856228325074789971}{262144}\cdot t^{135}-\frac{4979734104861794367}{131072}\cdot t^{133}+\frac{1197501135235128593001}{16777216}\cdot t^{131}-\frac{2068143798387504749769}{16777216}\cdot t^{129}+\frac{6586921410557705733945}{33554432}\cdot t^{127}-\frac{151528458234912638523}{524288}\cdot t^{125}+\frac{211696942473117915777075}{536870912}\cdot t^{123}-\frac{268193460610990804097325}{536870912}\cdot t^{121}+\frac{2528489371704803152147425}{4294967296}\cdot t^{119}-\frac{1388112062242139240914875}{2147483648}\cdot t^{117}+\frac{91004963823250124722814025}{137438953472}\cdot t^{115}-\frac{87079164031004749219809765}{137438953472}\cdot t^{113}+\frac{623297664109942402393761795}{1099511627776}\cdot t^{111}-\frac{130485029528366261282115505}{274877906944}\cdot t^{109}+\frac{6549906979619999953536090875}{17592186044416}\cdot t^{107}-\frac{4814843552350350554217377305}{17592186044416}\cdot t^{105}+\frac{26552576031186847713881803565}{140737488355328}\cdot t^{103}-\frac{8585945180710219312212410045}{70368744177664}\cdot t^{101}+\frac{1334022504787376971510209876775}{18014398509481984}\cdot t^{99}-\frac{760024881138122320376764791375}{18014398509481984}\cdot t^{97}+\frac{26017699664790820988691858693525}{1152921504606846976}\cdot t^{95}-\frac{1633298757063402144587969610975}{144115188075855872}\cdot t^{93}+\frac{98578080551363708942918374855675}{18446744073709551616}\cdot t^{91}-\frac{43637468281418103440455252045901}{18446744073709551616}\cdot t^{89}+\frac{145052076890041431465553459566305}{147573952589676412928}\cdot t^{87}-\frac{28278017577510467382341894513191}{73786976294838206464}\cdot t^{85}+\frac{661933468316865125099723486405231}{4722366482869645213696}\cdot t^{83}-\frac{227009520716686466653238674844731}{4722366482869645213696}\cdot t^{81}+\frac{583694417248155844500607111309257}{37778931862957161709568}\cdot t^{79}-\frac{43927737351949929259031089329945}{9444732965739290427392}\cdot t^{77}+\frac{792128151494545493203909988125653}{604462909807314587353088}\cdot t^{75}-\frac{208735857037232701755122782777455}{604462909807314587353088}\cdot t^{73}+\frac{411181515916127212646263017060315}{4835703278458516698824704}\cdot t^{71}-\frac{47257558095722974308607761397935}{2417851639229258349412352}\cdot t^{69}+\frac{1296582505795240750767451444022475}{309485009821345068724781056}\cdot t^{67}-\frac{258851905348819558603963025335995}{309485009821345068724781056}\cdot t^{65}+\frac{192275368464516203680067046370149}{1237940039285380274899124224}\cdot t^{63}-\frac{2072763452472690756666845113299}{77371252455336267181195264}\cdot t^{61}+\frac{84875383695144184809170868520479}{19807040628566084398385987584}\cdot t^{59}-\frac{12568005786797061406443746579025}{19807040628566084398385987584}\cdot t^{57}+\frac{13756523917475833787186614443093}{158456325028528675187087900672}\cdot t^{55}-\frac{867752098807174684958114753199}{79228162514264337593543950336}\cdot t^{53}+\frac{6445668171551698577985846867921}{5070602400912917605986812821504}\cdot t^{51}-\frac{686516442430864518490564010685}{5070602400912917605986812821504}\cdot t^{49}+\frac{535332839978271359301270730275}{40564819207303340847894502572032}\cdot t^{47}-\frac{11902476058668767060105078805}{10141204801825835211973625643008}\cdot t^{45}+\frac{61608129720737519608340967315}{649037107316853453566312041152512}\cdot t^{43}-\frac{4514519420835179646882641265}{649037107316853453566312041152512}\cdot t^{41}+\frac{2388144670941231437574755493}{5192296858534827628530496329220096}\cdot t^{39}-\frac{70926749138368603552528365}{2596148429267413814265248164610048}\cdot t^{37}+\frac{1927902857499241153862834607}{1329227995784915872903807060280344576}\cdot t^{35}-\frac{90960737119322369066049063}{1329227995784915872903807060280344576}\cdot t^{33}+\frac{60635875756661996367822933}{21267647932558653966460912964485513216}\cdot t^{31}-\frac{276841476303080540176749}{2658455991569831745807614120560689152}\cdot t^{29}+\frac{1125297451018882415031555}{340282366920938463463374607431768211456}\cdot t^{27}-\frac{30773674189629543665493}{340282366920938463463374607431768211456}\cdot t^{25}+\frac{5733788410323849583305}{2722258935367507707706996859454145691648}\cdot t^{23}-\frac{56126683545168405015}{1361129467683753853853498429727072845824}\cdot t^{21}+\frac{58201017265387848555}{87112285931760246646623899502532662132736}\cdot t^{19}-\frac{765862399780881975}{87112285931760246646623899502532662132736}\cdot t^{17}+\frac{63973804421966085}{696898287454081973172991196020261297061888}\cdot t^{15}-\frac{128673138501873}{174224571863520493293247799005065324265472}\cdot t^{13}+\frac{49134591391977}{11150372599265311570767859136324180752990208}\cdot t^{11}-\frac{206432136027}{11150372599265311570767859136324180752990208}\cdot t^9+\frac{4536624375}{89202980794122492566142873090593446023921664}\cdot t^7-\frac{3632067}{44601490397061246283071436545296723011960832}\cdot t^5+\frac{354321}{5708990770823839524233143877797980545530986496}\cdot t^3-\frac{81}{5708990770823839524233143877797980545530986496}\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.