Rule: Q[7, 84, 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.

• $P_1$:
  $64\cdot t^7-112\cdot t^5+56\cdot t^3-7\cdot t$
• $P_2$:
  $64\cdot t^{91}-1456\cdot t^{89}+16016\cdot t^{87}-113477\cdot t^{85}+\frac{2328235}{4}\cdot t^{83}-\frac{36851087}{16}\cdot t^{81}+\frac{58528197}{8}\cdot t^{79}-\frac{1226703231}{64}\cdot t^{77}+\frac{21622491891}{512}\cdot t^{75}-\frac{162608170725}{2048}\cdot t^{73}+\frac{263786588065}{2048}\cdot t^{71}-\frac{11918357660755}{65536}\cdot t^{69}+\frac{58988327156395}{262144}\cdot t^{67}-\frac{257244953338835}{1048576}\cdot t^{65}+\frac{31022118677225}{131072}\cdot t^{63}-\frac{212583150093405}{1048576}\cdot t^{61}+\frac{2593514431139541}{16777216}\cdot t^{59}-\frac{7054854040826319}{67108864}\cdot t^{57}+\frac{4284454737122833}{67108864}\cdot t^{55}-\frac{37207106927645655}{1073741824}\cdot t^{53}+\frac{72213230065205229}{4294967296}\cdot t^{51}-\frac{125267848072294785}{17179869184}\cdot t^{49}+\frac{24261361879614405}{8589934592}\cdot t^{47}-\frac{67075529902463355}{68719476736}\cdot t^{45}+\frac{165186006476215725}{549755813888}\cdot t^{43}-\frac{180803592543057939}{2199023255552}\cdot t^{41}+\frac{43863593457191571}{2199023255552}\cdot t^{39}-\frac{1203811953769590893}{281474976710656}\cdot t^{37}+\frac{909000863050507409}{1125899906842624}\cdot t^{35}-\frac{601619036168022145}{4503599627370496}\cdot t^{33}+\frac{21697735730649979}{1125899906842624}\cdot t^{31}-\frac{21697735730649979}{9007199254740992}\cdot t^{29}+\frac{74654921242744843}{288230376151711744}\cdot t^{27}-\frac{27381272054549049}{1152921504606846976}\cdot t^{25}+\frac{2119293502674075}{1152921504606846976}\cdot t^{23}-\frac{2188494923169555}{18446744073709551616}\cdot t^{21}+\frac{464226195823845}{73786976294838206464}\cdot t^{19}-\frac{79462141627505}{295147905179352825856}\cdot t^{17}+\frac{1341466144655}{147573952589676412928}\cdot t^{15}-\frac{277818432325}{1180591620717411303424}\cdot t^{13}+\frac{42489877885}{9444732965739290427392}\cdot t^{11}-\frac{2279944667}{37778931862957161709568}\cdot t^9+\frac{19941207}{37778931862957161709568}\cdot t^7-\frac{3246243}{1208925819614629174706176}\cdot t^5+\frac{31395}{4835703278458516698824704}\cdot t^3-\frac{91}{19342813113834066795298816}\cdot t$
• $P_3$:
  $64\cdot t^{183}-2944\cdot t^{181}+66604\cdot t^{179}-987900\cdot t^{177}+10805201\cdot t^{175}-92937460\cdot t^{173}+\frac{41898196165}{64}\cdot t^{171}-\frac{248552530071}{64}\cdot t^{169}+\frac{20277239924955}{1024}\cdot t^{167}-\frac{45126194103887}{512}\cdot t^{165}+\frac{5679262538529151}{16384}\cdot t^{163}-\frac{19930568288235111}{16384}\cdot t^{161}+\frac{125828575676490141}{32768}\cdot t^{159}-\frac{2810006828988345}{256}\cdot t^{157}+\frac{29961818242952328063}{1048576}\cdot t^{155}-\frac{71371818242710256601}{1048576}\cdot t^{153}+\frac{4999166397841263875667}{33554432}\cdot t^{151}-\frac{5045646743730944212185}{16777216}\cdot t^{149}+\frac{301517381274142111679925}{536870912}\cdot t^{147}-\frac{522342349679219622092505}{536870912}\cdot t^{145}+\frac{3366003884469818701370345}{2147483648}\cdot t^{143}-\frac{1263419949215372141748555}{536870912}\cdot t^{141}+\frac{906851283052194804593893715}{274877906944}\cdot t^{139}-\frac{1189101405516273851204846425}{274877906944}\cdot t^{137}+\frac{23369203730362161069875384635}{4398046511104}\cdot t^{135}-\frac{13462530990252386645045073267}{2199023255552}\cdot t^{133}+\frac{466141972775253790368710887299}{70368744177664}\cdot t^{131}-\frac{474188790692184757798662207539}{70368744177664}\cdot t^{129}+\frac{226963542860139423576224898625}{35184372088832}\cdot t^{127}-\frac{25577897188874967318589605251}{4398046511104}\cdot t^{125}+\frac{5563979760435441481284452514525}{1125899906842624}\cdot t^{123}-\frac{4458879381579084687391960334275}{1125899906842624}\cdot t^{121}+\frac{215796778687242015576613030890005}{72057594037927936}\cdot t^{119}-\frac{77029592579002517234194571386075}{36028797018963968}\cdot t^{117}+\frac{1661975719580872561636377732220095}{1152921504606846976}\cdot t^{115}-\frac{1058658436539037116724599973327155}{1152921504606846976}\cdot t^{113}+\frac{2549005881981893283084804543533945}{4611686018427387904}\cdot t^{111}-\frac{362552293054518217770159741308465}{1152921504606846976}\cdot t^{109}+\frac{49914722047385353408462198548050775}{295147905179352825856}\cdot t^{107}-\frac{25376488428664745288805037261703085}{295147905179352825856}\cdot t^{105}+\frac{195137024126023401069921747550136445}{4722366482869645213696}\cdot t^{103}-\frac{44325942127936395722838869622303585}{2361183241434822606848}\cdot t^{101}+\frac{609068116429253653244353502286721425}{75557863725914323419136}\cdot t^{99}-\frac{247148365680807997732330486043417625}{75557863725914323419136}\cdot t^{97}+\frac{189501566484534238544149970678850525}{151115727451828646838272}\cdot t^{95}-\frac{4288693991375005691729469339125775}{9444732965739290427392}\cdot t^{93}+\frac{750728519060763789595066377681303675}{4835703278458516698824704}\cdot t^{91}-\frac{242241778474299045389179683771645325}{4835703278458516698824704}\cdot t^{89}+\frac{2359606167765804962939664406738186125}{154742504910672534362390528}\cdot t^{87}-\frac{338604997294620127894252972445650175}{77371252455336267181195264}\cdot t^{85}+\frac{2930295848272384660992819123892601795}{2475880078570760549798248448}\cdot t^{83}-\frac{746235306807706818008667699168639695}{2475880078570760549798248448}\cdot t^{81}+\frac{715283065342162391318585905302480555}{9903520314283042199192993792}\cdot t^{79}-\frac{40289132186187381088677353551771125}{2475880078570760549798248448}\cdot t^{77}+\frac{17463540623773692235695988182407085165}{5070602400912917605986812821504}\cdot t^{75}-\frac{3468747723561553344713082356550141975}{5070602400912917605986812821504}\cdot t^{73}+\frac{10334829708178340549859267614321316225}{81129638414606681695789005144064}\cdot t^{71}-\frac{901070331004156179815162214347091393}{40564819207303340847894502572032}\cdot t^{69}+\frac{4702521961751076334817872856489682705}{1298074214633706907132624082305024}\cdot t^{67}-\frac{716318694142649127119407027735941009}{1298074214633706907132624082305024}\cdot t^{65}+\frac{101765921842062013698940607636766531}{1298074214633706907132624082305024}\cdot t^{63}-\frac{1682841649883377545354696077728827}{162259276829213363391578010288128}\cdot t^{61}+\frac{52979176116157716992371466082730491}{41538374868278621028243970633760768}\cdot t^{59}-\frac{6045211863916738672684794596828085}{41538374868278621028243970633760768}\cdot t^{57}+\frac{81759123475639595751220471734342027}{5316911983139663491615228241121378304}\cdot t^{55}-\frac{3990959221486239836745841340403597}{2658455991569831745807614120560689152}\cdot t^{53}+\frac{11492602444813467468288353189019849}{85070591730234615865843651857942052864}\cdot t^{51}-\frac{950823147979609053946315229005605}{85070591730234615865843651857942052864}\cdot t^{49}+\frac{288467648515850397095421318654675}{340282366920938463463374607431768211456}\cdot t^{47}-\frac{4998953538275215821134887408095}{85070591730234615865843651857942052864}\cdot t^{45}+\frac{80794540161617024446736012590995}{21778071482940061661655974875633165533184}\cdot t^{43}-\frac{4628414556026792947250416865745}{21778071482940061661655974875633165533184}\cdot t^{41}+\frac{3833405106294753600646101156405}{348449143727040986586495598010130648530944}\cdot t^{39}-\frac{89241607076182735269867469425}{174224571863520493293247799005065324265472}\cdot t^{37}+\frac{118981632787779136955298172545}{5575186299632655785383929568162090376495104}\cdot t^{35}-\frac{4410579526709379210553061241}{5575186299632655785383929568162090376495104}\cdot t^{33}+\frac{289057288433328327083818647}{11150372599265311570767859136324180752990208}\cdot t^{31}-\frac{259747083334073098593921}{348449143727040986586495598010130648530944}\cdot t^{29}+\frac{6655681501231706736320325}{356811923176489970264571492362373784095686656}\cdot t^{27}-\frac{143542046398474472746851}{356811923176489970264571492362373784095686656}\cdot t^{25}+\frac{84431403366077181014685}{11417981541647679048466287755595961091061972992}\cdot t^{23}-\frac{652727543675186218855}{5708990770823839524233143877797980545530986496}\cdot t^{21}+\frac{267442951850693473547}{182687704666362864775460604089535377456991567872}\cdot t^{19}-\frac{2782644819307308935}{182687704666362864775460604089535377456991567872}\cdot t^{17}+\frac{91938011802418767}{730750818665451459101842416358141509827966271488}\cdot t^{15}-\frac{146344885015237}{182687704666362864775460604089535377456991567872}\cdot t^{13}+\frac{353929056074659}{93536104789177786765035829293842113257979682750464}\cdot t^{11}-\frac{1177551306217}{93536104789177786765035829293842113257979682750464}\cdot t^9+\frac{40995442995}{1496577676626844588240573268701473812127674924007424}\cdot t^7-\frac{26001339}{748288838313422294120286634350736906063837462003712}\cdot t^5+\frac{502411}{23945242826029513411849172299223580994042798784118784}\cdot t^3-\frac{91}{23945242826029513411849172299223580994042798784118784}\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.