Rule: Q[2, 44, 92]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{46}-23\cdot t^{44}+\frac{989}{8}\cdot t^{42}-\frac{6601}{16}\cdot t^{40}+\frac{61295}{64}\cdot t^{38}-\frac{210197}{128}\cdot t^{36}+\frac{4414137}{2048}\cdot t^{34}-\frac{9070809}{4096}\cdot t^{32}+\frac{14799741}{8192}\cdot t^{30}-\frac{19332995}{16384}\cdot t^{28}+\frac{81198579}{131072}\cdot t^{26}-\frac{68544255}{262144}\cdot t^{24}+\frac{92736345}{1048576}\cdot t^{22}-\frac{49934955}{2097152}\cdot t^{20}+\frac{677688675}{134217728}\cdot t^{18}-\frac{222981435}{268435456}\cdot t^{16}+\frac{222981435}{2147483648}\cdot t^{14}-\frac{41158845}{4294967296}\cdot t^{12}+\frac{21559395}{34359738368}\cdot t^{10}-\frac{1891175}{68719476736}\cdot t^8+\frac{203665}{274877906944}\cdot t^6-\frac{5819}{549755813888}\cdot t^4+\frac{529}{8796093022208}\cdot t^2-\frac{1}{17592186044416}$
• $P_3$:
  $2\cdot t^{138}-69\cdot t^{136}+\frac{9315}{8}\cdot t^{134}-\frac{204953}{16}\cdot t^{132}+\frac{13224057}{128}\cdot t^{130}-\frac{166742433}{256}\cdot t^{128}+\frac{213901909}{64}\cdot t^{126}-\frac{1836943875}{128}\cdot t^{124}+\frac{107757953775}{2048}\cdot t^{122}-\frac{685065854275}{4096}\cdot t^{120}+\frac{244568509976175}{524288}\cdot t^{118}-\frac{1208487061106325}{1048576}\cdot t^{116}+\frac{21324361633807375}{8388608}\cdot t^{114}-\frac{84523208174371263}{16777216}\cdot t^{112}+\frac{302647616366297103}{33554432}\cdot t^{110}-\frac{983399707379919313}{67108864}\cdot t^{108}+\frac{46574454993780113037}{2147483648}\cdot t^{106}-\frac{126002353933099819665}{4294967296}\cdot t^{104}+\frac{1249756680862375248381}{34359738368}\cdot t^{102}-\frac{2847190032340599250071}{68719476736}\cdot t^{100}+\frac{23887441796755875064155}{549755813888}\cdot t^{98}-\frac{46209609629621764012995}{1099511627776}\cdot t^{96}+\frac{41284447474740447472425}{1099511627776}\cdot t^{94}-\frac{68224695618937805634015}{2199023255552}\cdot t^{92}+\frac{835054315382671504046745}{35184372088832}\cdot t^{90}-\frac{1183855763931893583613173}{70368744177664}\cdot t^{88}+\frac{12449999627283759994701171}{1125899906842624}\cdot t^{86}-\frac{15183432978886267194071665}{2251799813685248}\cdot t^{84}+\frac{68739542031685100569524447}{18014398509481984}\cdot t^{82}-\frac{72218924102254419168424767}{36028797018963968}\cdot t^{80}+\frac{70435740791087643386488353}{72057594037927936}\cdot t^{78}-\frac{63768022187409162824728527}{144115188075855872}\cdot t^{76}+\frac{1714517577680340698589399075}{9223372036854775808}\cdot t^{74}-\frac{1336482533135526761007205455}{18446744073709551616}\cdot t^{72}+\frac{3864309224767428055581919845}{147573952589676412928}\cdot t^{70}-\frac{2588712004941286755681091935}{295147905179352825856}\cdot t^{68}+\frac{6423840901150600467801228135}{2361183241434822606848}\cdot t^{66}-\frac{3687219355891902061395138975}{4722366482869645213696}\cdot t^{64}+\frac{489041725097241747090302643}{2361183241434822606848}\cdot t^{62}-\frac{239517716176867170097840533}{4722366482869645213696}\cdot t^{60}+\frac{865196648230724267496281109}{75557863725914323419136}\cdot t^{58}-\frac{359610273956597237659379601}{151115727451828646838272}\cdot t^{56}+\frac{2197618340845872007918430895}{4835703278458516698824704}\cdot t^{54}-\frac{769838885128627379028463797}{9671406556917033397649408}\cdot t^{52}+\frac{987240195048897393222188583}{77371252455336267181195264}\cdot t^{50}-\frac{288977118025065545208406455}{154742504910672534362390528}\cdot t^{48}+\frac{77024146770386090499783195}{309485009821345068724781056}\cdot t^{46}-\frac{18639231215185785285778725}{618970019642690137449562112}\cdot t^{44}+\frac{65306343442836121779061755}{19807040628566084398385987584}\cdot t^{42}-\frac{12893547742325590656219255}{39614081257132168796771975168}\cdot t^{40}+\frac{9142697490012691556228199}{316912650057057350374175801344}\cdot t^{38}-\frac{1448572534478008150558581}{633825300114114700748351602688}\cdot t^{36}+\frac{816279692952723734214585}{5070602400912917605986812821504}\cdot t^{34}-\frac{101649924028075031053137}{10141204801825835211973625643008}\cdot t^{32}+\frac{5557579620582585472041}{10141204801825835211973625643008}\cdot t^{30}-\frac{529583162092754584959}{20282409603651670423947251286016}\cdot t^{28}+\frac{348749887231813994973}{324518553658426726783156020576256}\cdot t^{26}-\frac{24549212334923012425}{649037107316853453566312041152512}\cdot t^{24}+\frac{11682038973170261085}{10384593717069655257060992658440192}\cdot t^{22}-\frac{578963956833797535}{20769187434139310514121985316880384}\cdot t^{20}+\frac{94019787861898745}{166153499473114484112975882535043072}\cdot t^{18}-\frac{3062599008488505}{332306998946228968225951765070086144}\cdot t^{16}+\frac{77994881370675}{664613997892457936451903530140172288}\cdot t^{14}-\frac{1502123641213}{1329227995784915872903807060280344576}\cdot t^{12}+\frac{1339731896217}{170141183460469231731687303715884105728}\cdot t^{10}-\frac{12705571197}{340282366920938463463374607431768211456}\cdot t^8+\frac{299457907}{2722258935367507707706996859454145691648}\cdot t^6-\frac{944265}{5444517870735015415413993718908291383296}\cdot t^4+\frac{4761}{43556142965880123323311949751266331066368}\cdot t^2-\frac{1}{87112285931760246646623899502532662132736}$

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.