Rule: Q[1, 6, 70, 78]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{7}{4}\cdot t^5+\frac{7}{8}\cdot t^3-\frac{7}{64}\cdot t$
• $P_3$:
  $t^{77}-\frac{77}{4}\cdot t^{75}+\frac{2849}{16}\cdot t^{73}-\frac{16863}{16}\cdot t^{71}+\frac{574035}{128}\cdot t^{69}-\frac{14963179}{1024}\cdot t^{67}+\frac{155322013}{4096}\cdot t^{65}-\frac{41207881}{512}\cdot t^{63}+\frac{1166362197}{8192}\cdot t^{61}-\frac{6975303335}{32768}\cdot t^{59}+\frac{35626101511}{131072}\cdot t^{57}-\frac{39159268603}{131072}\cdot t^{55}+\frac{298212891669}{1048576}\cdot t^{53}-\frac{15805283258457}{67108864}\cdot t^{51}+\frac{45695546835675}{268435456}\cdot t^{49}-\frac{14445688999665}{134217728}\cdot t^{47}+\frac{255996554239965}{4294967296}\cdot t^{45}-\frac{496934487642285}{17179869184}\cdot t^{43}+\frac{845069382939705}{68719476736}\cdot t^{41}-\frac{314408754088275}{68719476736}\cdot t^{39}+\frac{817462760629515}{549755813888}\cdot t^{37}-\frac{1851803396528085}{4398046511104}\cdot t^{35}+\frac{1821195075924315}{17592186044416}\cdot t^{33}-\frac{96778482295495}{4398046511104}\cdot t^{31}+\frac{283031410486825}{70368744177664}\cdot t^{29}-\frac{176785773319463}{281474976710656}\cdot t^{27}+\frac{93592468227951}{1125899906842624}\cdot t^{25}-\frac{10399163136439}{1125899906842624}\cdot t^{23}+\frac{7670519747869}{9007199254740992}\cdot t^{21}-\frac{9257523833635}{144115188075855872}\cdot t^{19}+\frac{2245441951137}{576460752303423488}\cdot t^{17}-\frac{53537886633}{288230376151711744}\cdot t^{15}+\frac{124921735477}{18446744073709551616}\cdot t^{13}-\frac{13421343481}{73786976294838206464}\cdot t^{11}+\frac{1009813805}{295147905179352825856}\cdot t^9-\frac{12365067}{295147905179352825856}\cdot t^7+\frac{703703}{2361183241434822606848}\cdot t^5-\frac{19019}{18889465931478580854784}\cdot t^3+\frac{77}{75557863725914323419136}\cdot t$
• $P_4$:
  $t^{155}-39\cdot t^{153}+\frac{11933}{16}\cdot t^{151}-\frac{74575}{8}\cdot t^{149}+\frac{21925201}{256}\cdot t^{147}-\frac{157892357}{256}\cdot t^{145}+\frac{3712292871}{1024}\cdot t^{143}-\frac{4578200913}{256}\cdot t^{141}+\frac{2475783819795}{32768}\cdot t^{139}-\frac{9097031315801}{32768}\cdot t^{137}+\frac{941564862089995}{1048576}\cdot t^{135}-\frac{1353423396303051}{524288}\cdot t^{133}+\frac{111543232238351949}{16777216}\cdot t^{131}-\frac{259059182252309565}{16777216}\cdot t^{129}+\frac{272782297176711153}{8388608}\cdot t^{127}-\frac{65418107818300821}{1048576}\cdot t^{125}+\frac{58776556851658768725}{536870912}\cdot t^{123}-\frac{94667991899363808075}{536870912}\cdot t^{121}+\frac{2245856055517127472375}{8589934592}\cdot t^{119}-\frac{1536728284692834181025}{4294967296}\cdot t^{117}+\frac{62252913397370248127575}{137438953472}\cdot t^{115}-\frac{73045757084510992542475}{137438953472}\cdot t^{113}+\frac{318315945812248362224675}{549755813888}\cdot t^{111}-\frac{80615488022053093198375}{137438953472}\cdot t^{109}+\frac{9732572891996606701629525}{17592186044416}\cdot t^{107}-\frac{8556401093221846669840695}{17592186044416}\cdot t^{105}+\frac{1796693361043457944428034905}{4503599627370496}\cdot t^{103}-\frac{688045910845490919164448005}{2251799813685248}\cdot t^{101}+\frac{15756644263315869470620168875}{72057594037927936}\cdot t^{99}-\frac{10541939579000899928936097251}{72057594037927936}\cdot t^{97}+\frac{13193319385440308464083136249}{144115188075855872}\cdot t^{95}-\frac{120687497681832755845834817}{2251799813685248}\cdot t^{93}+\frac{541647468079633962871448393693}{18446744073709551616}\cdot t^{91}-\frac{277718512185223736492476817115}{18446744073709551616}\cdot t^{89}+\frac{2132263369960892640583741273917}{295147905179352825856}\cdot t^{87}-\frac{478759123904575808060773770855}{147573952589676412928}\cdot t^{85}+\frac{6437011090780279706344798982377}{4722366482869645213696}\cdot t^{83}-\frac{2529834582862554341504087498989}{4722366482869645213696}\cdot t^{81}+\frac{3718682004261846580798866052635}{18889465931478580854784}\cdot t^{79}-\frac{319294766372707700067744657441}{4722366482869645213696}\cdot t^{77}+\frac{13111269488556761851941194706123}{604462909807314587353088}\cdot t^{75}-\frac{3926258804840951735220531994065}{604462909807314587353088}\cdot t^{73}+\frac{35092995324509984928597630615285}{19342813113834066795298816}\cdot t^{71}-\frac{4567293150272236616357420081325}{9671406556917033397649408}\cdot t^{69}+\frac{35418078398655472394686856310315}{309485009821345068724781056}\cdot t^{67}-\frac{7981935345492453463289849511435}{309485009821345068724781056}\cdot t^{65}+\frac{1670796012824586527773632521055}{309485009821345068724781056}\cdot t^{63}-\frac{40549688708401326877836112245}{38685626227668133590597632}\cdot t^{61}+\frac{3733317647766926652328285360425}{19807040628566084398385987584}\cdot t^{59}-\frac{620716144434296034290190463335}{19807040628566084398385987584}\cdot t^{57}+\frac{1523968645343088436893061804599}{316912650057057350374175801344}\cdot t^{55}-\frac{107695746354236009342079032073}{158456325028528675187087900672}\cdot t^{53}+\frac{447638765307458929439695041087}{5070602400912917605986812821504}\cdot t^{51}-\frac{53305753395905979876536847075}{5070602400912917605986812821504}\cdot t^{49}+\frac{23215663018751941049014254783}{20282409603651670423947251286016}\cdot t^{47}-\frac{576079417632526683719255559}{5070602400912917605986812821504}\cdot t^{45}+\frac{6650386202193182192323650909}{649037107316853453566312041152512}\cdot t^{43}-\frac{543027057469674801540568383}{649037107316853453566312041152512}\cdot t^{41}+\frac{2558877581312892107438948835}{41538374868278621028243970633760768}\cdot t^{39}-\frac{84565951859041357534064079}{20769187434139310514121985316880384}\cdot t^{37}+\frac{159762217086057902438084625}{664613997892457936451903530140172288}\cdot t^{35}-\frac{8377447050790998264815913}{664613997892457936451903530140172288}\cdot t^{33}+\frac{775406648614418254491057}{1329227995784915872903807060280344576}\cdot t^{31}-\frac{1965232661777760283095}{83076749736557242056487941267521536}\cdot t^{29}+\frac{283668356776079655051573}{340282366920938463463374607431768211456}\cdot t^{27}-\frac{8604944318385733588083}{340282366920938463463374607431768211456}\cdot t^{25}+\frac{3555462556306275002505}{5444517870735015415413993718908291383296}\cdot t^{23}-\frac{38576781540015958755}{2722258935367507707706996859454145691648}\cdot t^{21}+\frac{22162630700686938525}{87112285931760246646623899502532662132736}\cdot t^{19}-\frac{323059718055378465}{87112285931760246646623899502532662132736}\cdot t^{17}+\frac{14942999648079315}{348449143727040986586495598010130648530944}\cdot t^{15}-\frac{33278523759405}{87112285931760246646623899502532662132736}\cdot t^{13}+\frac{28135567080855}{11150372599265311570767859136324180752990208}\cdot t^{11}-\frac{130841006725}{11150372599265311570767859136324180752990208}\cdot t^9+\frac{12729403115}{356811923176489970264571492362373784095686656}\cdot t^7-\frac{11278267}{178405961588244985132285746181186892047843328}\cdot t^5+\frac{304381}{5708990770823839524233143877797980545530986496}\cdot t^3-\frac{77}{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.