Rule: Q[2, 3, 4, 16, 96]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^5-3\cdot t^3+1\cdot t$
• $P_3$:
  $2\cdot t^9-5\cdot t^7+\frac{17}{4}\cdot t^5-\frac{11}{8}\cdot t^3+\frac{1}{8}\cdot t$
• $P_4$:
  $2\cdot t^{25}-13\cdot t^{23}+\frac{149}{4}\cdot t^{21}-\frac{495}{8}\cdot t^{19}+\frac{2109}{32}\cdot t^{17}-\frac{3009}{64}\cdot t^{15}+\frac{5831}{256}\cdot t^{13}-\frac{3809}{512}\cdot t^{11}+\frac{52195}{32768}\cdot t^9-\frac{13871}{65536}\cdot t^7+\frac{4147}{262144}\cdot t^5-\frac{289}{524288}\cdot t^3+\frac{3}{524288}\cdot t$
• $P_5$:
  $2\cdot t^{121}-61\cdot t^{119}+\frac{3629}{4}\cdot t^{117}-\frac{70151}{8}\cdot t^{115}+\frac{1981795}{32}\cdot t^{113}-\frac{21807079}{64}\cdot t^{111}+\frac{389221833}{256}\cdot t^{109}-\frac{2895883551}{512}\cdot t^{107}+\frac{586438977663}{32768}\cdot t^{105}-\frac{3204720010635}{65536}\cdot t^{103}+\frac{30603768273975}{262144}\cdot t^{101}-\frac{128880494308605}{524288}\cdot t^{99}+\frac{482340302169635}{1048576}\cdot t^{97}-\frac{1614282242385365}{2097152}\cdot t^{95}+\frac{9712635613875775}{8388608}\cdot t^{93}-\frac{26377727534962545}{16777216}\cdot t^{91}+\frac{2076959328948572565}{1073741824}\cdot t^{89}-\frac{4644346064223755505}{2147483648}\cdot t^{87}+\frac{18923856021362172265}{8589934592}\cdot t^{85}-\frac{35200019455364238475}{17179869184}\cdot t^{83}+\frac{119769123509987101997}{68719476736}\cdot t^{81}-\frac{186627398670186546177}{137438953472}\cdot t^{79}+\frac{533320579386136664343}{549755813888}\cdot t^{77}-\frac{699363701301123909297}{1099511627776}\cdot t^{75}+\frac{53901836188093738912275}{140737488355328}\cdot t^{73}-\frac{59635557563598111914559}{281474976710656}\cdot t^{71}+\frac{121255218957043674406323}{1125899906842624}\cdot t^{69}-\frac{113271772351415041184961}{2251799813685248}\cdot t^{67}+\frac{24302141255266869613971}{1125899906842624}\cdot t^{65}-\frac{38303496973894837215795}{4503599627370496}\cdot t^{63}+\frac{55404729117515649339633}{18014398509481984}\cdot t^{61}-\frac{36743976325269331111983}{36028797018963968}\cdot t^{59}+\frac{1428641970988219629741489}{4611686018427387904}\cdot t^{57}-\frac{794077718622481025045901}{9223372036854775808}\cdot t^{55}+\frac{806458444254358996914765}{36893488147419103232}\cdot t^{53}-\frac{373494435077747298677895}{73786976294838206464}\cdot t^{51}+\frac{314907072712610467512735}{295147905179352825856}\cdot t^{49}-\frac{120572925290771870748195}{590295810358705651712}\cdot t^{47}+\frac{83646525801137747023485}{2361183241434822606848}\cdot t^{45}-\frac{26210381190861779509675}{4722366482869645213696}\cdot t^{43}+\frac{236646965565453412821005}{302231454903657293676544}\cdot t^{41}-\frac{59902326323398723207505}{604462909807314587353088}\cdot t^{39}+\frac{27094917633505325556645}{2417851639229258349412352}\cdot t^{37}-\frac{5449325011811526437655}{4835703278458516698824704}\cdot t^{35}+\frac{969467439183376876575}{9671406556917033397649408}\cdot t^{33}-\frac{151646776665757488661}{19342813113834066795298816}\cdot t^{31}+\frac{41425368775966162127}{77371252455336267181195264}\cdot t^{29}-\frac{4901302339200697409}{154742504910672534362390528}\cdot t^{27}+\frac{15927024196385019627}{9903520314283042199192993792}\cdot t^{25}-\frac{1373223551914438575}{19807040628566084398385987584}\cdot t^{23}+\frac{198501359253020967}{79228162514264337593543950336}\cdot t^{21}-\frac{11844132949743237}{158456325028528675187087900672}\cdot t^{19}+\frac{1145399201036343}{633825300114114700748351602688}\cdot t^{17}-\frac{43861638984867}{1267650600228229401496703205376}\cdot t^{15}+\frac{2584081406165}{5070602400912917605986812821504}\cdot t^{13}-\frac{56372133923}{10141204801825835211973625643008}\cdot t^{11}+\frac{110715608719}{2596148429267413814265248164610048}\cdot t^9-\frac{1109776843}{5192296858534827628530496329220096}\cdot t^7+\frac{12959999}{20769187434139310514121985316880384}\cdot t^5-\frac{36005}{41538374868278621028243970633760768}\cdot t^3+\frac{15}{41538374868278621028243970633760768}\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.