Rule: Q[25, 26, 100]

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.

• $P_1$:
  $16777216\cdot t^{25}-104857600\cdot t^{23}+288358400\cdot t^{21}-458752000\cdot t^{19}+466944000\cdot t^{17}-317521920\cdot t^{15}+146227200\cdot t^{13}-45260800\cdot t^{11}+9152000\cdot t^9-1144000\cdot t^7+80080\cdot t^5-2600\cdot t^3+25\cdot t$
• $P_2$:
  $16777216\cdot t^{51}-218103808\cdot t^{49}+1334837248\cdot t^{47}-5112856576\cdot t^{45}+13743882240\cdot t^{43}-27557691392\cdot t^{41}+42764230656\cdot t^{39}-52596883456\cdot t^{37}+52086158592\cdot t^{35}-41960439040\cdot t^{33}+27672014656\cdot t^{31}-14985215488\cdot t^{29}+6665772148\cdot t^{27}-2430180396\cdot t^{25}+\frac{1445389725}{2}\cdot t^{23}-173996955\cdot t^{21}+\frac{4295336595}{128}\cdot t^{19}-\frac{654116895}{128}\cdot t^{17}+\frac{2469143955}{4096}\cdot t^{15}-\frac{54977475}{1024}\cdot t^{13}+\frac{228524205}{65536}\cdot t^{11}-\frac{10311015}{65536}\cdot t^9+\frac{2408445}{524288}\cdot t^7-\frac{20345}{262144}\cdot t^5+\frac{10425}{16777216}\cdot t^3-\frac{25}{16777216}\cdot t$
• $P_3$:
  $16777216\cdot t^{151}-637534208\cdot t^{149}+11873026048\cdot t^{147}-144442392576\cdot t^{145}+1290963517440\cdot t^{143}-9038617116672\cdot t^{141}+51622262788096\cdot t^{139}-247285405085696\cdot t^{137}+1013867645155072\cdot t^{135}-3612932437655040\cdot t^{133}+11325542260341936\cdot t^{131}-31533181626334128\cdot t^{129}+78597505211011488\cdot t^{127}-176530896107870976\cdot t^{125}+359241990860545875\cdot t^{123}-665470212117248525\cdot t^{121}+\frac{36051392299335270275}{32}\cdot t^{119}-\frac{27984790296424495325}{16}\cdot t^{117}+\frac{1278707024293771711925}{512}\cdot t^{115}-\frac{1683644684657804064625}{512}\cdot t^{113}+\frac{8194739402960808657575}{2048}\cdot t^{111}-\frac{2308252984419292520775}{512}\cdot t^{109}+\frac{4940063693633725025754825}{1048576}\cdot t^{107}-\frac{4795039824054092259988275}{1048576}\cdot t^{105}+\frac{69255558079323114511852125}{16777216}\cdot t^{103}-\frac{29101380383857944054491313}{8388608}\cdot t^{101}+\frac{729275262800639054371888533}{268435456}\cdot t^{99}-\frac{532580728707621582402818173}{268435456}\cdot t^{97}+\frac{725842035100660412331273877}{536870912}\cdot t^{95}-\frac{28859698334701912216217105}{33554432}\cdot t^{93}+\frac{8778727806923385239576535573}{17179869184}\cdot t^{91}-\frac{4872012421162051103536919139}{17179869184}\cdot t^{89}+\frac{161670435210737962580657306721}{1099511627776}\cdot t^{87}-\frac{39157960503625018286413569611}{549755813888}\cdot t^{85}+\frac{567065067302761290319042343315}{17592186044416}\cdot t^{83}-\frac{239695840498625458468156800031}{17592186044416}\cdot t^{81}+\frac{378433594245813640480213805727}{70368744177664}\cdot t^{79}-\frac{34855615330353192817650554073}{17592186044416}\cdot t^{77}+\frac{3067022418547598412941913424551}{4503599627370496}\cdot t^{75}-\frac{982932912828242262157236567525}{4503599627370496}\cdot t^{73}+\frac{4696216025822648205170029117065}{72057594037927936}\cdot t^{71}-\frac{652778177416988396472006001785}{36028797018963968}\cdot t^{69}+\frac{5401347048939809160436774632045}{1152921504606846976}\cdot t^{67}-\frac{1297687446774960056621309176365}{1152921504606846976}\cdot t^{65}+\frac{289338619406933701802328843075}{1152921504606846976}\cdot t^{63}-\frac{7473918419925581128020443655}{144115188075855872}\cdot t^{61}+\frac{365914600253239763902333852065}{36893488147419103232}\cdot t^{59}-\frac{64658580105017370596000623215}{36893488147419103232}\cdot t^{57}+\frac{337208966418358692898811048835}{1180591620717411303424}\cdot t^{55}-\frac{25293539610008240577673349925}{590295810358705651712}\cdot t^{53}+\frac{111524500956003556848040284957}{18889465931478580854784}\cdot t^{51}-\frac{14080127480772067682420728041}{18889465931478580854784}\cdot t^{49}+\frac{6497943959174009046707695059}{75557863725914323419136}\cdot t^{47}-\frac{170775489047807720883743127}{18889465931478580854784}\cdot t^{45}+\frac{8348283221999940479018751135}{9671406556917033397649408}\cdot t^{43}-\frac{721323531971420190158872533}{9671406556917033397649408}\cdot t^{41}+\frac{898834062384800001723147279}{154742504910672534362390528}\cdot t^{39}-\frac{31408080401934091587353427}{77371252455336267181195264}\cdot t^{37}+\frac{62716417270012991109130623}{2475880078570760549798248448}\cdot t^{35}-\frac{3474851581190951342136135}{2475880078570760549798248448}\cdot t^{33}+\frac{339733107429060288033453}{4951760157141521099596496896}\cdot t^{31}-\frac{28414006261022525187}{9671406556917033397649408}\cdot t^{29}+\frac{17319507161059192305993}{158456325028528675187087900672}\cdot t^{27}-\frac{554516262416857347711}{158456325028528675187087900672}\cdot t^{25}+\frac{1934187295125890706525}{20282409603651670423947251286016}\cdot t^{23}-\frac{22140539838608222295}{10141204801825835211973625643008}\cdot t^{21}+\frac{13417317296027233695}{324518553658426726783156020576256}\cdot t^{19}-\frac{206272026382117995}{324518553658426726783156020576256}\cdot t^{17}+\frac{10061156298538935}{1298074214633706907132624082305024}\cdot t^{15}-\frac{23625146842325}{324518553658426726783156020576256}\cdot t^{13}+\frac{42116519771365}{83076749736557242056487941267521536}\cdot t^{11}-\frac{206471989295}{83076749736557242056487941267521536}\cdot t^9+\frac{10587366295}{1329227995784915872903807060280344576}\cdot t^7-\frac{9887695}{664613997892457936451903530140172288}\cdot t^5+\frac{281275}{21267647932558653966460912964485513216}\cdot t^3-\frac{75}{21267647932558653966460912964485513216}\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.