Rule: Q[2, 39, 40, 80]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{41}-21\cdot t^{39}+\frac{409}{4}\cdot t^{37}-\frac{2451}{8}\cdot t^{35}+\frac{10115}{16}\cdot t^{33}-\frac{30481}{32}\cdot t^{31}+\frac{138787}{128}\cdot t^{29}-\frac{243629}{256}\cdot t^{27}+\frac{21352149}{32768}\cdot t^{25}-\frac{22931025}{65536}\cdot t^{23}+\frac{38629305}{262144}\cdot t^{21}-\frac{25398555}{524288}\cdot t^{19}+\frac{25820145}{2097152}\cdot t^{17}-\frac{9992005}{4194304}\cdot t^{15}+\frac{5757475}{16777216}\cdot t^{13}-\frac{1196069}{33554432}\cdot t^{11}+\frac{5475173}{2147483648}\cdot t^9-\frac{503481}{4294967296}\cdot t^7+\frac{53333}{17179869184}\cdot t^5-\frac{1335}{34359738368}\cdot t^3+\frac{5}{34359738368}\cdot t$
• $P_3$:
  $2\cdot t^{81}-41\cdot t^{79}+\frac{1619}{4}\cdot t^{77}-\frac{20501}{8}\cdot t^{75}+\frac{748325}{64}\cdot t^{73}-\frac{5242641}{128}\cdot t^{71}+\frac{58666377}{512}\cdot t^{69}-\frac{269253939}{1024}\cdot t^{67}+\frac{2066445557}{4096}\cdot t^{65}-\frac{6724376945}{8192}\cdot t^{63}+\frac{37510410223}{32768}\cdot t^{61}-\frac{90412119473}{65536}\cdot t^{59}+\frac{758074648799}{524288}\cdot t^{57}-\frac{1388647909691}{1048576}\cdot t^{55}+\frac{4462127961615}{4194304}\cdot t^{53}-\frac{6304519296045}{8388608}\cdot t^{51}+\frac{1004471202260565}{2147483648}\cdot t^{49}-\frac{1102606665411405}{4294967296}\cdot t^{47}+\frac{2135390661379815}{17179869184}\cdot t^{45}-\frac{1823451793911825}{34359738368}\cdot t^{43}+\frac{5486885897842965}{274877906944}\cdot t^{41}-\frac{3630225306480465}{549755813888}\cdot t^{39}+\frac{4214986347647985}{2199023255552}\cdot t^{37}-\frac{2140586247441915}{4398046511104}\cdot t^{35}+\frac{3789443170401525}{35184372088832}\cdot t^{33}-\frac{1454693706607869}{70368744177664}\cdot t^{31}+\frac{963279451051883}{281474976710656}\cdot t^{29}-\frac{273214376948261}{562949953421312}\cdot t^{27}+\frac{263374723516751}{4503599627370496}\cdot t^{25}-\frac{53406232536475}{9007199254740992}\cdot t^{23}+\frac{18010091821799}{36028797018963968}\cdot t^{21}-\frac{2489098783589}{72057594037927936}\cdot t^{19}+\frac{17729302242597}{9223372036854775808}\cdot t^{17}-\frac{1554115724493}{18446744073709551616}\cdot t^{15}+\frac{208607759535}{73786976294838206464}\cdot t^{13}-\frac{10327828537}{147573952589676412928}\cdot t^{11}+\frac{1433973073}{1180591620717411303424}\cdot t^9-\frac{32436781}{2361183241434822606848}\cdot t^7+\frac{853333}{9444732965739290427392}\cdot t^5-\frac{5335}{18889465931478580854784}\cdot t^3+\frac{5}{18889465931478580854784}\cdot t$
• $P_4$:
  $2\cdot t^{161}-81\cdot t^{159}+\frac{6439}{4}\cdot t^{157}-\frac{167401}{8}\cdot t^{155}+\frac{12806255}{64}\cdot t^{153}-\frac{192128475}{128}\cdot t^{151}+\frac{4709277015}{512}\cdot t^{149}-\frac{48478482805}{1024}\cdot t^{147}+\frac{3422251230685}{16384}\cdot t^{145}-\frac{26288099475925}{32768}\cdot t^{143}+\frac{355843116267639}{131072}\cdot t^{141}-\frac{2142708152262769}{262144}\cdot t^{139}+\frac{46281794982445477}{2097152}\cdot t^{137}-\frac{225603189738697553}{4194304}\cdot t^{135}+\frac{1996499276837967465}{16777216}\cdot t^{133}-\frac{8056969431650256051}{33554432}\cdot t^{131}+\frac{119096809058262192729}{268435456}\cdot t^{129}-\frac{404437194701562179793}{536870912}\cdot t^{127}+\frac{2531807846747674058319}{2147483648}\cdot t^{125}-\frac{7323622721576115152625}{4294967296}\cdot t^{123}+\frac{78492669628068769701675}{34359738368}\cdot t^{121}-\frac{195208108651199323349175}{68719476736}\cdot t^{119}+\frac{902799438356571894774075}{274877906944}\cdot t^{117}-\frac{1944119493147736451257425}{549755813888}\cdot t^{115}+\frac{31232137474628978778408375}{8796093022208}\cdot t^{113}-\frac{58554546017461977562494415}{17592186044416}\cdot t^{111}+\frac{205193854851678483303194605}{70368744177664}\cdot t^{109}-\frac{336306619031482510347745435}{140737488355328}\cdot t^{107}+\frac{2063903085864023322293740035}{1125899906842624}\cdot t^{105}-\frac{2966052652604670030919377575}{2251799813685248}\cdot t^{103}+\frac{7989467781858758352261939175}{9007199254740992}\cdot t^{101}-\frac{10088440227215774559291164525}{18014398509481984}\cdot t^{99}+\frac{3058450922593637565324812483925}{9223372036854775808}\cdot t^{97}-\frac{3397527831163171031651709632325}{18446744073709551616}\cdot t^{95}+\frac{7081597081556792206486113683875}{73786976294838206464}\cdot t^{93}-\frac{6924048911454637546804027477901}{147573952589676412928}\cdot t^{91}+\frac{25404814424791327688867058012659}{1180591620717411303424}\cdot t^{89}-\frac{21858384449082619276864288806543}{2361183241434822606848}\cdot t^{87}+\frac{35274309386964915399767248392779}{9444732965739290427392}\cdot t^{85}-\frac{26683508892182962986676117846385}{18889465931478580854784}\cdot t^{83}+\frac{151328182249521885611268510339437}{302231454903657293676544}\cdot t^{81}-\frac{100484756071401773790789561432837}{604462909807314587353088}\cdot t^{79}+\frac{124927126687683927920148206517783}{2417851639229258349412352}\cdot t^{77}-\frac{72651222352834000361680587588657}{4835703278458516698824704}\cdot t^{75}+\frac{157987019489711717517852023664525}{38685626227668133590597632}\cdot t^{73}-\frac{80223679513315995657289440206265}{77371252455336267181195264}\cdot t^{71}+\frac{76026053160252160729821319495905}{309485009821345068724781056}\cdot t^{69}-\frac{33579970528794511770009796835835}{618970019642690137449562112}\cdot t^{67}+\frac{110475490088815037403272648946045}{9903520314283042199192993792}\cdot t^{65}-\frac{42245102387634092476058629997325}{19807040628566084398385987584}\cdot t^{63}+\frac{29999365402708598602296323003427}{79228162514264337593543950336}\cdot t^{61}-\frac{9874898316955742515076531619837}{158456325028528675187087900672}\cdot t^{59}+\frac{12033215105408721725473313898231}{1267650600228229401496703205376}\cdot t^{57}-\frac{3386265948098457463936032229779}{2535301200456458802993406410752}\cdot t^{55}+\frac{1756887805768709318039626918935}{10141204801825835211973625643008}\cdot t^{53}-\frac{419186604295786284641203245765}{20282409603651670423947251286016}\cdot t^{51}+\frac{734095119443767883989295652615}{324518553658426726783156020576256}\cdot t^{49}-\frac{147032625055264717707486432255}{649037107316853453566312041152512}\cdot t^{47}+\frac{53728827786514416141177496365}{2596148429267413814265248164610048}\cdot t^{45}-\frac{8925556477561474265545182075}{5192296858534827628530496329220096}\cdot t^{43}+\frac{5372765906987562300190478043}{41538374868278621028243970633760768}\cdot t^{41}-\frac{729479117051855607860351103}{83076749736557242056487941267521536}\cdot t^{39}+\frac{177913712417927350359355887}{332306998946228968225951765070086144}\cdot t^{37}-\frac{19388199704953125203757093}{664613997892457936451903530140172288}\cdot t^{35}+\frac{240314141072589391861970085}{170141183460469231731687303715884105728}\cdot t^{33}-\frac{20546715126111124428769269}{340282366920938463463374607431768211456}\cdot t^{31}+\frac{3079779814215851981266563}{1361129467683753853853498429727072845824}\cdot t^{29}-\frac{200656880843174467399821}{2722258935367507707706996859454145691648}\cdot t^{27}+\frac{45028816093825229950011}{21778071482940061661655974875633165533184}\cdot t^{25}-\frac{2151232752627229029975}{43556142965880123323311949751266331066368}\cdot t^{23}+\frac{172768064274430960995}{174224571863520493293247799005065324265472}\cdot t^{21}-\frac{5741171266700702745}{348449143727040986586495598010130648530944}\cdot t^{19}+\frac{1239474295500810345}{5575186299632655785383929568162090376495104}\cdot t^{17}-\frac{26539968981178305}{11150372599265311570767859136324180752990208}\cdot t^{15}+\frac{875700550388475}{44601490397061246283071436545296723011960832}\cdot t^{13}-\frac{10713617118477}{89202980794122492566142873090593446023921664}\cdot t^{11}+\frac{369174764673}{713623846352979940529142984724747568191373312}\cdot t^9-\frac{2079369981}{1427247692705959881058285969449495136382746624}\cdot t^7+\frac{13653333}{5708990770823839524233143877797980545530986496}\cdot t^5-\frac{21335}{11417981541647679048466287755595961091061972992}\cdot t^3+\frac{5}{11417981541647679048466287755595961091061972992}\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.