Rule: Q[4, 5, 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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^9-20\cdot t^7+17\cdot t^5-\frac{11}{2}\cdot t^3+\frac{1}{2}\cdot t$
• $P_3$:
  $8\cdot t^{105}-212\cdot t^{103}+2729\cdot t^{101}-\frac{45475}{2}\cdot t^{99}+\frac{551397}{4}\cdot t^{97}-\frac{5185523}{8}\cdot t^{95}+\frac{78738489}{32}\cdot t^{93}-\frac{495996311}{64}\cdot t^{91}+\frac{169227701565}{8192}\cdot t^{89}-\frac{774940501049}{16384}\cdot t^{87}+\frac{6167065054865}{65536}\cdot t^{85}-\frac{21517480484227}{131072}\cdot t^{83}+\frac{132627804399181}{524288}\cdot t^{81}-\frac{363174311654145}{1048576}\cdot t^{79}+\frac{1775769255599607}{4194304}\cdot t^{77}-\frac{3891345891643089}{8388608}\cdot t^{75}+\frac{245375037647722305}{536870912}\cdot t^{73}-\frac{435920992725079845}{1073741824}\cdot t^{71}+\frac{1399308329876925825}{4294967296}\cdot t^{69}-\frac{2032305951671654715}{8589934592}\cdot t^{67}+\frac{668542055517477405}{4294967296}\cdot t^{65}-\frac{1595309072237665785}{17179869184}\cdot t^{63}+\frac{3453509739570767955}{68719476736}\cdot t^{61}-\frac{3391712638553005325}{137438953472}\cdot t^{59}+\frac{96702549458435866335}{8796093022208}\cdot t^{57}-\frac{78131077082491025411}{17592186044416}\cdot t^{55}+\frac{114401678289846564771}{70368744177664}\cdot t^{53}-\frac{75813613146463561289}{140737488355328}\cdot t^{51}+\frac{90831358131970133225}{562949953421312}\cdot t^{49}-\frac{49102534548213417061}{1125899906842624}\cdot t^{47}+\frac{47810870588951242843}{4503599627370496}\cdot t^{45}-\frac{20912083510386246717}{9007199254740992}\cdot t^{43}+\frac{524448142346769520187}{1152921504606846976}\cdot t^{41}-\frac{183511843411256606295}{2305843009213693952}\cdot t^{39}+\frac{114249764157885247619}{9223372036854775808}\cdot t^{37}-\frac{31501581633302067105}{18446744073709551616}\cdot t^{35}+\frac{7655223063576631361}{36893488147419103232}\cdot t^{33}-\frac{1630178531207405179}{73786976294838206464}\cdot t^{31}+\frac{604380570885840385}{295147905179352825856}\cdot t^{29}-\frac{96778404611898863}{590295810358705651712}\cdot t^{27}+\frac{1698147689556987963}{151115727451828646838272}\cdot t^{25}-\frac{197193307569703935}{302231454903657293676544}\cdot t^{23}+\frac{38310829751664855}{1208925819614629174706176}\cdot t^{21}-\frac{3066637183365525}{2417851639229258349412352}\cdot t^{19}+\frac{397195570405935}{9671406556917033397649408}\cdot t^{17}-\frac{20342231142555}{19342813113834066795298816}\cdot t^{15}+\frac{1600854439485}{77371252455336267181195264}\cdot t^{13}-\frac{46600814715}{154742504910672534362390528}\cdot t^{11}+\frac{30506801325}{9903520314283042199192993792}\cdot t^9-\frac{407436705}{19807040628566084398385987584}\cdot t^7+\frac{6336733}{79228162514264337593543950336}\cdot t^5-\frac{23439}{158456325028528675187087900672}\cdot t^3+\frac{13}{158456325028528675187087900672}\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.