Rule: Q[1, 2, 66, 70]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $t^{69}-\frac{69}{4}\cdot t^{67}+\frac{2277}{16}\cdot t^{65}-\frac{1495}{2}\cdot t^{63}+\frac{44919}{16}\cdot t^{61}-\frac{8220177}{1024}\cdot t^{59}+\frac{74416523}{4096}\cdot t^{57}-\frac{136830381}{4096}\cdot t^{55}+\frac{3331034685}{65536}\cdot t^{53}-\frac{17000614059}{262144}\cdot t^{51}+\frac{73477230255}{1048576}\cdot t^{49}-\frac{33859413315}{524288}\cdot t^{47}+\frac{214046934465}{4194304}\cdot t^{45}-\frac{1164321236925}{33554432}\cdot t^{43}+\frac{2730862537515}{134217728}\cdot t^{41}-\frac{1382288444915}{134217728}\cdot t^{39}+\frac{19325957314755}{4294967296}\cdot t^{37}-\frac{29120107628115}{17179869184}\cdot t^{35}+\frac{37748287666075}{68719476736}\cdot t^{33}-\frac{2622512616801}{17179869184}\cdot t^{31}+\frac{4977421905357}{137438953472}\cdot t^{29}-\frac{16038359472817}{2199023255552}\cdot t^{27}+\frac{10888712137251}{8796093022208}\cdot t^{25}-\frac{1543768261425}{8796093022208}\cdot t^{23}+\frac{2893136075115}{140737488355328}\cdot t^{21}-\frac{1104651955953}{562949953421312}\cdot t^{19}+\frac{337916787957}{2251799813685248}\cdot t^{17}-\frac{10131543907}{1125899906842624}\cdot t^{15}+\frac{3706662405}{9007199254740992}\cdot t^{13}-\frac{996964371}{72057594037927936}\cdot t^{11}+\frac{93731693}{288230376151711744}\cdot t^9-\frac{1432233}{288230376151711744}\cdot t^7+\frac{812889}{18446744073709551616}\cdot t^5-\frac{13685}{73786976294838206464}\cdot t^3+\frac{69}{295147905179352825856}\cdot t$
• $P_4$:
  $t^{139}-35\cdot t^{137}+\frac{9589}{16}\cdot t^{135}-\frac{53533}{8}\cdot t^{133}+\frac{14025781}{256}\cdot t^{131}-\frac{89787269}{256}\cdot t^{129}+\frac{233966655}{128}\cdot t^{127}-\frac{127574421}{16}\cdot t^{125}+\frac{121673673975}{4096}\cdot t^{123}-\frac{393118997225}{4096}\cdot t^{121}+\frac{285374606513425}{1048576}\cdot t^{119}-\frac{358519325077375}{524288}\cdot t^{117}+\frac{25742414630150075}{16777216}\cdot t^{115}-\frac{51915049884194431}{16777216}\cdot t^{113}+\frac{378437945154723509}{67108864}\cdot t^{111}-\frac{156512358693493341}{16777216}\cdot t^{109}+\frac{60402330565548500925}{4294967296}\cdot t^{107}-\frac{83253729230883207279}{4294967296}\cdot t^{105}+\frac{1683399564639864676059}{68719476736}\cdot t^{103}-\frac{977661895163015354487}{34359738368}\cdot t^{101}+\frac{33468995086627211277855}{1099511627776}\cdot t^{99}-\frac{33036453321042901658775}{1099511627776}\cdot t^{97}+\frac{60267105703400662374315}{2199023255552}\cdot t^{95}-\frac{3178928469699611015205}{137438953472}\cdot t^{93}+\frac{1272330727068962936648385}{70368744177664}\cdot t^{91}-\frac{922061898532201109008599}{70368744177664}\cdot t^{89}+\frac{19837455677989199458490205}{2251799813685248}\cdot t^{87}-\frac{6189870119781255730780111}{1125899906842624}\cdot t^{85}+\frac{114781952234853259428385243}{36028797018963968}\cdot t^{83}-\frac{61778256599190978358246343}{36028797018963968}\cdot t^{81}+\frac{123543591580185096022420683}{144115188075855872}\cdot t^{79}-\frac{14342704030482580383126405}{36028797018963968}\cdot t^{77}+\frac{3166970729477560722283297731}{18446744073709551616}\cdot t^{75}-\frac{1268026608269740399216484985}{18446744073709551616}\cdot t^{73}+\frac{7538518730578140421962932835}{295147905179352825856}\cdot t^{71}-\frac{1298977731527984469506853315}{147573952589676412928}\cdot t^{69}+\frac{13277049493942026275111558475}{4722366482869645213696}\cdot t^{67}-\frac{3927279122206380411880619595}{4722366482869645213696}\cdot t^{65}+\frac{1074721785105578654233646457}{4722366482869645213696}\cdot t^{63}-\frac{33972933370774459621860489}{590295810358705651712}\cdot t^{61}+\frac{2029843573385322397164574029}{151115727451828646838272}\cdot t^{59}-\frac{436597777305556015719180675}{151115727451828646838272}\cdot t^{57}+\frac{5529659429970285060240605169}{9671406556917033397649408}\cdot t^{55}-\frac{502489860213845653196867127}{4835703278458516698824704}\cdot t^{53}+\frac{2678369463521404777803988179}{154742504910672534362390528}\cdot t^{51}-\frac{407952612935119150334139015}{154742504910672534362390528}\cdot t^{49}+\frac{226702275955391684804326425}{618970019642690137449562112}\cdot t^{47}-\frac{7161546808282332317531085}{154742504910672534362390528}\cdot t^{45}+\frac{210050028808555817370268395}{39614081257132168796771975168}\cdot t^{43}-\frac{21744473764098760346702745}{39614081257132168796771975168}\cdot t^{41}+\frac{32415636102642545573382849}{633825300114114700748351602688}\cdot t^{39}-\frac{1353249312467704441473645}{316912650057057350374175801344}\cdot t^{37}+\frac{3224220286159847495102661}{10141204801825835211973625643008}\cdot t^{35}-\frac{212897886556824691740189}{10141204801825835211973625643008}\cdot t^{33}+\frac{24779166358810714187403}{20282409603651670423947251286016}\cdot t^{31}-\frac{39434228461679376891}{633825300114114700748351602688}\cdot t^{29}+\frac{1784932997721603028485}{649037107316853453566312041152512}\cdot t^{27}-\frac{67841214609030724771}{649037107316853453566312041152512}\cdot t^{25}+\frac{70173205753769438515}{20769187434139310514121985316880384}\cdot t^{23}-\frac{952153974558274345}{10384593717069655257060992658440192}\cdot t^{21}+\frac{683526009238563645}{332306998946228968225951765070086144}\cdot t^{19}-\frac{12440992562189025}{332306998946228968225951765070086144}\cdot t^{17}+\frac{718080410223345}{1329227995784915872903807060280344576}\cdot t^{15}-\frac{1994458480139}{332306998946228968225951765070086144}\cdot t^{13}+\frac{16816371245401}{340282366920938463463374607431768211456}\cdot t^{11}-\frac{97450298891}{340282366920938463463374607431768211456}\cdot t^9+\frac{5905458725}{5444517870735015415413993718908291383296}\cdot t^7-\frac{6516797}{2722258935367507707706996859454145691648}\cdot t^5+\frac{219029}{87112285931760246646623899502532662132736}\cdot t^3-\frac{69}{87112285931760246646623899502532662132736}\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.