Rule: Q[1, 70, 72]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{71}-\frac{71}{4}\cdot t^{69}+\frac{1207}{8}\cdot t^{67}-\frac{52327}{64}\cdot t^{65}+\frac{50765}{16}\cdot t^{63}-\frac{600873}{64}\cdot t^{61}+\frac{2819481}{128}\cdot t^{59}-\frac{689161713}{16384}\cdot t^{57}+\frac{4364690849}{65536}\cdot t^{55}-\frac{23231419035}{262144}\cdot t^{53}+\frac{52480156443}{524288}\cdot t^{51}-\frac{405528481605}{4194304}\cdot t^{49}+\frac{336794840655}{4194304}\cdot t^{47}-\frac{965716771215}{16777216}\cdot t^{45}+\frac{1198069678575}{33554432}\cdot t^{43}-\frac{10303399235745}{536870912}\cdot t^{41}+\frac{38403578969595}{4294967296}\cdot t^{39}-\frac{61997934676405}{17179869184}\cdot t^{37}+\frac{43281577038245}{34359738368}\cdot t^{35}-\frac{104261288816825}{274877906944}\cdot t^{33}+\frac{13492637376295}{137438953472}\cdot t^{31}-\frac{11950621676147}{549755813888}\cdot t^{29}+\frac{4500883488419}{1099511627776}\cdot t^{27}-\frac{22895798615001}{35184372088832}\cdot t^{25}+\frac{12178616284575}{140737488355328}\cdot t^{23}-\frac{5358591165213}{562949953421312}\cdot t^{21}+\frac{961798414269}{1125899906842624}\cdot t^{19}-\frac{553762723367}{9007199254740992}\cdot t^{17}+\frac{31275635539}{9007199254740992}\cdot t^{15}-\frac{5392350955}{36028797018963968}\cdot t^{13}+\frac{341953963}{72057594037927936}\cdot t^{11}-\frac{121338503}{1152921504606846976}\cdot t^9+\frac{28001193}{18446744073709551616}\cdot t^7-\frac{937839}{73786976294838206464}\cdot t^5+\frac{7455}{147573952589676412928}\cdot t^3-\frac{71}{1180591620717411303424}\cdot t$
• $P_3$:
  $t^{143}-36\cdot t^{141}+\frac{10151}{16}\cdot t^{139}-\frac{116725}{16}\cdot t^{137}+\frac{7879007}{128}\cdot t^{135}-\frac{26006787}{64}\cdot t^{133}+\frac{8951571783}{4096}\cdot t^{131}-\frac{40325461319}{4096}\cdot t^{129}+\frac{155267814845}{4096}\cdot t^{127}-\frac{32429389421}{256}\cdot t^{125}+\frac{24368774982825}{65536}\cdot t^{123}-\frac{63435424211575}{65536}\cdot t^{121}+\frac{1180758385821025}{524288}\cdot t^{119}-\frac{1235731535913875}{262144}\cdot t^{117}+\frac{2395670632327203825}{268435456}\cdot t^{115}-\frac{4121278782569141325}{268435456}\cdot t^{113}+\frac{103479681312029165825}{4294967296}\cdot t^{111}-\frac{37157713756240285439}{1073741824}\cdot t^{109}+\frac{3135322230737453491515}{68719476736}\cdot t^{107}-\frac{3803735133311961787929}{68719476736}\cdot t^{105}+\frac{34043187623216375006403}{549755813888}\cdot t^{103}-\frac{17592602953453658244699}{274877906944}\cdot t^{101}+\frac{1076774259332288948269605}{17592186044416}\cdot t^{99}-\frac{954131593540982480257725}{17592186044416}\cdot t^{97}+\frac{3137004348100896212376255}{70368744177664}\cdot t^{95}-\frac{299259435478337227723683}{8796093022208}\cdot t^{93}+\frac{27164041586766859189881039}{1125899906842624}\cdot t^{91}-\frac{17910751388376109403519449}{1125899906842624}\cdot t^{89}+\frac{87884180277552778573290375}{9007199254740992}\cdot t^{87}-\frac{25079512270460574370283609}{4503599627370496}\cdot t^{85}+\frac{1705238382511193482400820449}{576460752303423488}\cdot t^{83}-\frac{843120164768602744789142069}{576460752303423488}\cdot t^{81}+\frac{12415633888334416460650670139}{18446744073709551616}\cdot t^{79}-\frac{1329190592347944238099860855}{4611686018427387904}\cdot t^{77}+\frac{33889563082842791515188432981}{295147905179352825856}\cdot t^{75}-\frac{12554638691168741332325928495}{295147905179352825856}\cdot t^{73}+\frac{34581058280644819030971605085}{2361183241434822606848}\cdot t^{71}-\frac{5529307323962167915017921345}{1180591620717411303424}\cdot t^{69}+\frac{105024070293169447020323854425}{75557863725914323419136}\cdot t^{67}-\frac{28900331416438748829814134345}{75557863725914323419136}\cdot t^{65}+\frac{14732045547378651490292370615}{151115727451828646838272}\cdot t^{63}-\frac{54275914510117058606563485}{2361183241434822606848}\cdot t^{61}+\frac{12106983749844270652379300979}{2417851639229258349412352}\cdot t^{59}-\frac{2432816588247637749541217085}{2417851639229258349412352}\cdot t^{57}+\frac{3601476087104027362843509243}{19342813113834066795298816}\cdot t^{55}-\frac{306280809669134216233654281}{9671406556917033397649408}\cdot t^{53}+\frac{12232266700799896375224512601}{2475880078570760549798248448}\cdot t^{51}-\frac{1746315446888636325684981765}{2475880078570760549798248448}\cdot t^{49}+\frac{3640893178898037540291170175}{39614081257132168796771975168}\cdot t^{47}-\frac{107949748614509844305890965}{9903520314283042199192993792}\cdot t^{45}+\frac{743371645942971549762258429}{633825300114114700748351602688}\cdot t^{43}-\frac{72311802863667939592117119}{633825300114114700748351602688}\cdot t^{41}+\frac{50675050129300458689942037}{5070602400912917605986812821504}\cdot t^{39}-\frac{1989956257742830708977525}{2535301200456458802993406410752}\cdot t^{37}+\frac{8923768678511363350839111}{162259276829213363391578010288128}\cdot t^{35}-\frac{554766625338993592840287}{162259276829213363391578010288128}\cdot t^{33}+\frac{121631134042251716650563}{649037107316853453566312041152512}\cdot t^{31}-\frac{729526261823925823353}{81129638414606681695789005144064}\cdot t^{29}+\frac{3890421348712377805995}{10384593717069655257060992658440192}\cdot t^{27}-\frac{139412152814141319021}{10384593717069655257060992658440192}\cdot t^{25}+\frac{33999595469733972195}{83076749736557242056487941267521536}\cdot t^{23}-\frac{435187481791633285}{41538374868278621028243970633760768}\cdot t^{21}+\frac{1179100845817789895}{5316911983139663491615228241121378304}\cdot t^{19}-\frac{20253793835207075}{5316911983139663491615228241121378304}\cdot t^{17}+\frac{17655403634255145}{340282366920938463463374607431768211456}\cdot t^{15}-\frac{46294546333705}{85070591730234615865843651857942052864}\cdot t^{13}+\frac{23034237106895}{5444517870735015415413993718908291383296}\cdot t^{11}-\frac{126045516941}{5444517870735015415413993718908291383296}\cdot t^9+\frac{3606668295}{43556142965880123323311949751266331066368}\cdot t^7-\frac{3758811}{21778071482940061661655974875633165533184}\cdot t^5+\frac{238631}{1393796574908163946345982392040522594123776}\cdot t^3-\frac{71}{1393796574908163946345982392040522594123776}\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.