Rule: Q[1, 12, 14, 26, 52]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-\frac{13}{4}\cdot t^{11}+\frac{65}{16}\cdot t^9-\frac{39}{16}\cdot t^7+\frac{91}{128}\cdot t^5-\frac{91}{1024}\cdot t^3+\frac{13}{4096}\cdot t$
• $P_3$:
  $t^{27}-7\cdot t^{25}+\frac{349}{16}\cdot t^{23}-\frac{319}{8}\cdot t^{21}+\frac{12145}{256}\cdot t^{19}-\frac{9861}{256}\cdot t^{17}+\frac{22287}{1024}\cdot t^{15}-\frac{2193}{256}\cdot t^{13}+\frac{75803}{32768}\cdot t^{11}-\frac{13585}{32768}\cdot t^9+\frac{48763}{1048576}\cdot t^7-\frac{1547}{524288}\cdot t^5+\frac{1469}{16777216}\cdot t^3-\frac{13}{16777216}\cdot t$
• $P_4$:
  $t^{53}-\frac{27}{2}\cdot t^{51}+86\cdot t^{49}-\frac{1375}{4}\cdot t^{47}+\frac{247549}{256}\cdot t^{45}-\frac{1042107}{512}\cdot t^{43}+\frac{3407019}{1024}\cdot t^{41}-\frac{8862601}{2048}\cdot t^{39}+\frac{298290785}{65536}\cdot t^{37}-\frac{512962931}{131072}\cdot t^{35}+\frac{363083331}{131072}\cdot t^{33}-\frac{212381221}{131072}\cdot t^{31}+\frac{3289500799}{4194304}\cdot t^{29}-\frac{2632267505}{8388608}\cdot t^{27}+\frac{1735430499}{16777216}\cdot t^{25}-\frac{937382805}{33554432}\cdot t^{23}+\frac{13165769595}{2147483648}\cdot t^{21}-\frac{4643330505}{4294967296}\cdot t^{19}+\frac{324111975}{2147483648}\cdot t^{17}-\frac{140500215}{8589934592}\cdot t^{15}+\frac{1474166715}{1099511627776}\cdot t^{13}-\frac{176498205}{2199023255552}\cdot t^{11}+\frac{14697345}{4398046511104}\cdot t^9-\frac{792675}{8796093022208}\cdot t^7+\frac{396045}{281474976710656}\cdot t^5-\frac{5863}{562949953421312}\cdot t^3+\frac{13}{562949953421312}\cdot t$
• $P_5$:
  $t^{105}-\frac{53}{2}\cdot t^{103}+\frac{2729}{8}\cdot t^{101}-\frac{45475}{16}\cdot t^{99}+\frac{551397}{32}\cdot t^{97}-\frac{5185523}{64}\cdot t^{95}+\frac{78738489}{256}\cdot t^{93}-\frac{495996311}{512}\cdot t^{91}+\frac{169227701565}{65536}\cdot t^{89}-\frac{774940501049}{131072}\cdot t^{87}+\frac{6167065054865}{524288}\cdot t^{85}-\frac{21517480484227}{1048576}\cdot t^{83}+\frac{132627804399181}{4194304}\cdot t^{81}-\frac{363174311654145}{8388608}\cdot t^{79}+\frac{1775769255599607}{33554432}\cdot t^{77}-\frac{3891345891643089}{67108864}\cdot t^{75}+\frac{245375037647722305}{4294967296}\cdot t^{73}-\frac{435920992725079845}{8589934592}\cdot t^{71}+\frac{1399308329876925825}{34359738368}\cdot t^{69}-\frac{2032305951671654715}{68719476736}\cdot t^{67}+\frac{668542055517477405}{34359738368}\cdot t^{65}-\frac{1595309072237665785}{137438953472}\cdot t^{63}+\frac{3453509739570767955}{549755813888}\cdot t^{61}-\frac{3391712638553005325}{1099511627776}\cdot t^{59}+\frac{96702549458435866335}{70368744177664}\cdot t^{57}-\frac{78131077082491025411}{140737488355328}\cdot t^{55}+\frac{114401678289846564771}{562949953421312}\cdot t^{53}-\frac{75813613146463561289}{1125899906842624}\cdot t^{51}+\frac{90831358131970133225}{4503599627370496}\cdot t^{49}-\frac{49102534548213417061}{9007199254740992}\cdot t^{47}+\frac{47810870588951242843}{36028797018963968}\cdot t^{45}-\frac{20912083510386246717}{72057594037927936}\cdot t^{43}+\frac{524448142346769520187}{9223372036854775808}\cdot t^{41}-\frac{183511843411256606295}{18446744073709551616}\cdot t^{39}+\frac{114249764157885247619}{73786976294838206464}\cdot t^{37}-\frac{31501581633302067105}{147573952589676412928}\cdot t^{35}+\frac{7655223063576631361}{295147905179352825856}\cdot t^{33}-\frac{1630178531207405179}{590295810358705651712}\cdot t^{31}+\frac{604380570885840385}{2361183241434822606848}\cdot t^{29}-\frac{96778404611898863}{4722366482869645213696}\cdot t^{27}+\frac{1698147689556987963}{1208925819614629174706176}\cdot t^{25}-\frac{197193307569703935}{2417851639229258349412352}\cdot t^{23}+\frac{38310829751664855}{9671406556917033397649408}\cdot t^{21}-\frac{3066637183365525}{19342813113834066795298816}\cdot t^{19}+\frac{397195570405935}{77371252455336267181195264}\cdot t^{17}-\frac{20342231142555}{154742504910672534362390528}\cdot t^{15}+\frac{1600854439485}{618970019642690137449562112}\cdot t^{13}-\frac{46600814715}{1237940039285380274899124224}\cdot t^{11}+\frac{30506801325}{79228162514264337593543950336}\cdot t^9-\frac{407436705}{158456325028528675187087900672}\cdot t^7+\frac{6336733}{633825300114114700748351602688}\cdot t^5-\frac{23439}{1267650600228229401496703205376}\cdot t^3+\frac{13}{1267650600228229401496703205376}\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.