Rule: Q[1, 16, 68, 86]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{17}-\frac{17}{4}\cdot t^{15}+\frac{119}{16}\cdot t^{13}-\frac{221}{32}\cdot t^{11}+\frac{935}{256}\cdot t^9-\frac{561}{512}\cdot t^7+\frac{357}{2048}\cdot t^5-\frac{51}{4096}\cdot t^3+\frac{17}{65536}\cdot t$
• $P_3$:
  $t^{85}-\frac{85}{4}\cdot t^{83}+\frac{3485}{16}\cdot t^{81}-\frac{11475}{8}\cdot t^{79}+\frac{436475}{64}\cdot t^{77}-\frac{25542517}{1024}\cdot t^{75}+\frac{299073775}{4096}\cdot t^{73}-\frac{719748975}{4096}\cdot t^{71}+\frac{23228262375}{65536}\cdot t^{69}-\frac{159337729625}{262144}\cdot t^{67}+\frac{939455253869}{1048576}\cdot t^{65}-\frac{150035851355}{131072}\cdot t^{63}+\frac{1337990948385}{1048576}\cdot t^{61}-\frac{10463775365575}{8388608}\cdot t^{59}+\frac{36023178371225}{33554432}\cdot t^{57}-\frac{27377615562131}{33554432}\cdot t^{55}+\frac{589213900141515}{1073741824}\cdot t^{53}-\frac{1404734869195515}{4294967296}\cdot t^{51}+\frac{2970210544318875}{17179869184}\cdot t^{49}-\frac{696365151538875}{8589934592}\cdot t^{47}+\frac{2316217627118535}{68719476736}\cdot t^{45}-\frac{54596558353508325}{4398046511104}\cdot t^{43}+\frac{71140969975783575}{17592186044416}\cdot t^{41}-\frac{20454276079993875}{17592186044416}\cdot t^{39}+\frac{82823052323909625}{281474976710656}\cdot t^{37}-\frac{73546870463631747}{1125899906842624}\cdot t^{35}+\frac{57053960789909895}{4503599627370496}\cdot t^{33}-\frac{2404573060111145}{1125899906842624}\cdot t^{31}+\frac{2802321987347575}{9007199254740992}\cdot t^{29}-\frac{2802321987347575}{72057594037927936}\cdot t^{27}+\frac{1192260627344241}{288230376151711744}\cdot t^{25}-\frac{106833389546975}{288230376151711744}\cdot t^{23}+\frac{509978255761975}{18446744073709551616}\cdot t^{21}-\frac{124819852808875}{73786976294838206464}\cdot t^{19}+\frac{24618448477875}{295147905179352825856}\cdot t^{17}-\frac{478301284713}{147573952589676412928}\cdot t^{15}+\frac{113881258265}{1180591620717411303424}\cdot t^{13}-\frac{40012333985}{18889465931478580854784}\cdot t^{11}+\frac{2464365475}{75557863725914323419136}\cdot t^9-\frac{24726075}{75557863725914323419136}\cdot t^7+\frac{2307767}{1208925819614629174706176}\cdot t^5-\frac{25585}{4835703278458516698824704}\cdot t^3+\frac{85}{19342813113834066795298816}\cdot t$
• $P_4$:
  $t^{171}-43\cdot t^{169}+\frac{14533}{16}\cdot t^{167}-\frac{100513}{8}\cdot t^{165}+\frac{32767405}{256}\cdot t^{163}-\frac{262180773}{256}\cdot t^{161}+\frac{3431560923}{512}\cdot t^{159}-\frac{590228829}{16}\cdot t^{157}+\frac{2855286803707}{16384}\cdot t^{155}-\frac{11758282323645}{16384}\cdot t^{153}+\frac{2734317888106805}{1048576}\cdot t^{151}-\frac{4425960286160335}{524288}\cdot t^{149}+\frac{411791376500705695}{16777216}\cdot t^{147}-\frac{1082466680511616715}{16777216}\cdot t^{145}+\frac{10348144642162472775}{67108864}\cdot t^{143}-\frac{5648251461743701965}{16777216}\cdot t^{141}+\frac{2895813117756326081895}{4294967296}\cdot t^{139}-\frac{5338683331102852522645}{4294967296}\cdot t^{137}+\frac{145414468284289344669865}{68719476736}\cdot t^{135}-\frac{114602933366360084069025}{34359738368}\cdot t^{133}+\frac{5364881319019023236027901}{1099511627776}\cdot t^{131}-\frac{7299267690458757844363533}{1099511627776}\cdot t^{129}+\frac{4626735412261449805741059}{549755813888}\cdot t^{127}-\frac{684264258349208623419021}{68719476736}\cdot t^{125}+\frac{193705299622964434640414625}{17592186044416}\cdot t^{123}-\frac{200451131941872322700096895}{17592186044416}\cdot t^{121}+\frac{6218696253241790615433041895}{562949953421312}\cdot t^{119}-\frac{2826887925810581455689189785}{281474976710656}\cdot t^{117}+\frac{77190902255616865720309548265}{9007199254740992}\cdot t^{115}-\frac{61867386342903766934314770325}{9007199254740992}\cdot t^{113}+\frac{186414205792787467714863070955}{36028797018963968}\cdot t^{111}-\frac{33011727390674754083547512635}{9007199254740992}\cdot t^{109}+\frac{11263398877247986648665183189195}{4611686018427387904}\cdot t^{107}-\frac{7063739304352555487196433129065}{4611686018427387904}\cdot t^{105}+\frac{66722071116571152204075145267275}{73786976294838206464}\cdot t^{103}-\frac{18543220605630736674814609400375}{36893488147419103232}\cdot t^{101}+\frac{310569837155201522912584653643275}{1180591620717411303424}\cdot t^{99}-\frac{153065471570744781519554939130275}{1180591620717411303424}\cdot t^{97}+\frac{142070111443865511544461061713475}{2361183241434822606848}\cdot t^{95}-\frac{3879791120738722335771043755875}{147573952589676412928}\cdot t^{93}+\frac{817063454842829288298357862437575}{75557863725914323419136}\cdot t^{91}-\frac{316283231045139783894305182032225}{75557863725914323419136}\cdot t^{89}+\frac{29487611407800465607000476638122725}{19342813113834066795298816}\cdot t^{87}-\frac{5049695238890843616490479105477975}{9671406556917033397649408}\cdot t^{85}+\frac{52023573006425390493044440660978375}{309485009821345068724781056}\cdot t^{83}-\frac{15735466841200393192740689963513251}{309485009821345068724781056}\cdot t^{81}+\frac{17874962859750790315843115102245707}{1237940039285380274899124224}\cdot t^{79}-\frac{1190731697931856816026160684908093}{309485009821345068724781056}\cdot t^{77}+\frac{76149518419357353459239553485323641}{79228162514264337593543950336}\cdot t^{75}-\frac{17819221377452261255406366077137275}{79228162514264337593543950336}\cdot t^{73}+\frac{62434241437939776267644794218291891}{1267650600228229401496703205376}\cdot t^{71}-\frac{6390607141031379564360645041613219}{633825300114114700748351602688}\cdot t^{69}+\frac{39090819438122221483089595628968503}{20282409603651670423947251286016}\cdot t^{67}-\frac{6968540082657791815258412622585591}{20282409603651670423947251286016}\cdot t^{65}+\frac{1156893558781277681209969862124705}{20282409603651670423947251286016}\cdot t^{63}-\frac{22324674844440851968980800327541}{2535301200456458802993406410752}\cdot t^{61}+\frac{819074356807718391359251172869623}{649037107316853453566312041152512}\cdot t^{59}-\frac{108782753729537366773600828120953}{649037107316853453566312041152512}\cdot t^{57}+\frac{427599219587975144931148299947607}{20769187434139310514121985316880384}\cdot t^{55}-\frac{24238089000477722858210675599185}{10384593717069655257060992658440192}\cdot t^{53}+\frac{80964313622962801188582506698305}{332306998946228968225951765070086144}\cdot t^{51}-\frac{7762247578403617098858698777085}{332306998946228968225951765070086144}\cdot t^{49}+\frac{2726335865080800903816813251415}{1329227995784915872903807060280344576}\cdot t^{47}-\frac{54646295763532749318326551995}{332306998946228968225951765070086144}\cdot t^{45}+\frac{4082724118058249586614352235575}{340282366920938463463374607431768211456}\cdot t^{43}-\frac{270069239114517998892991936605}{340282366920938463463374607431768211456}\cdot t^{41}+\frac{258090293156432322746830454715}{5444517870735015415413993718908291383296}\cdot t^{39}-\frac{6927680396563292915527469295}{2722258935367507707706996859454145691648}\cdot t^{37}+\frac{10642482686980845551133377955}{87112285931760246646623899502532662132736}\cdot t^{35}-\frac{454286087948431007875766475}{87112285931760246646623899502532662132736}\cdot t^{33}+\frac{34263781896742122328922241}{174224571863520493293247799005065324265472}\cdot t^{31}-\frac{17707396499370661358877}{2722258935367507707706996859454145691648}\cdot t^{29}+\frac{1043258911580494224156441}{5575186299632655785383929568162090376495104}\cdot t^{27}-\frac{25855003481002044847407}{5575186299632655785383929568162090376495104}\cdot t^{25}+\frac{34936777962261824141025}{356811923176489970264571492362373784095686656}\cdot t^{23}-\frac{310119073470640117827}{178405961588244985132285746181186892047843328}\cdot t^{21}+\frac{145846588185583111827}{5708990770823839524233143877797980545530986496}\cdot t^{19}-\frac{1741240170272253807}{5708990770823839524233143877797980545530986496}\cdot t^{17}+\frac{65995619866847091}{22835963083295358096932575511191922182123945984}\cdot t^{15}-\frac{120480260906745}{5708990770823839524233143877797980545530986496}\cdot t^{13}+\frac{167054404931127}{1461501637330902918203684832716283019655932542976}\cdot t^{11}-\frac{637214360101}{1461501637330902918203684832716283019655932542976}\cdot t^9+\frac{25430299201}{23384026197294446691258957323460528314494920687616}\cdot t^7-\frac{18487721}{11692013098647223345629478661730264157247460343808}\cdot t^5+\frac{409445}{374144419156711147060143317175368453031918731001856}\cdot t^3-\frac{85}{374144419156711147060143317175368453031918731001856}\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.