Rule: Q[2, 12, 84]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{14}-7\cdot t^{12}+\frac{77}{8}\cdot t^{10}-\frac{105}{16}\cdot t^8+\frac{147}{64}\cdot t^6-\frac{49}{128}\cdot t^4+\frac{49}{2048}\cdot t^2-\frac{1}{4096}$
• $P_3$:
  $2\cdot t^{98}-49\cdot t^{96}+\frac{4655}{8}\cdot t^{94}-\frac{71393}{16}\cdot t^{92}+\frac{3179267}{128}\cdot t^{90}-\frac{27382719}{256}\cdot t^{88}+\frac{379786407}{1024}\cdot t^{86}-\frac{2179151205}{2048}\cdot t^{84}+\frac{84405790007}{32768}\cdot t^{82}-\frac{349952095647}{65536}\cdot t^{80}+\frac{2513292323283}{262144}\cdot t^{78}-\frac{7886537979957}{524288}\cdot t^{76}+\frac{87118733499525}{4194304}\cdot t^{74}-\frac{212948144056305}{8388608}\cdot t^{72}+\frac{925672544571285}{33554432}\cdot t^{70}-\frac{1795581682843095}{67108864}\cdot t^{68}+\frac{49882135042885005}{2147483648}\cdot t^{66}-\frac{77703107964406925}{4294967296}\cdot t^{64}+\frac{108784351150169695}{8589934592}\cdot t^{62}-\frac{137049439057275745}{17179869184}\cdot t^{60}+\frac{621993608029174535}{137438953472}\cdot t^{58}-\frac{635841332141141315}{274877906944}\cdot t^{56}+\frac{1171286664470523475}{1099511627776}\cdot t^{54}-\frac{971658676439025561}{2199023255552}\cdot t^{52}+\frac{5803691013324990513}{35184372088832}\cdot t^{50}-\frac{3895628214423623769}{70368744177664}\cdot t^{48}+\frac{4694731437895136337}{281474976710656}\cdot t^{46}-\frac{2534714156610050135}{562949953421312}\cdot t^{44}+\frac{4893550188067566179}{4503599627370496}\cdot t^{42}-\frac{2105620545690242119}{9007199254740992}\cdot t^{40}+\frac{1610180417292538091}{36028797018963968}\cdot t^{38}-\frac{544996068058090649}{72057594037927936}\cdot t^{36}+\frac{5202235195099956195}{4611686018427387904}\cdot t^{34}-\frac{1360584589487680851}{9223372036854775808}\cdot t^{32}+\frac{2481066016124594493}{147573952589676412928}\cdot t^{30}-\frac{489462003181042451}{295147905179352825856}\cdot t^{28}+\frac{331571034412964241}{2361183241434822606848}\cdot t^{26}-\frac{47745053692606725}{4722366482869645213696}\cdot t^{24}+\frac{11559328788736365}{18889465931478580854784}\cdot t^{22}-\frac{1160454128725815}{37778931862957161709568}\cdot t^{20}+\frac{760297532613465}{604462909807314587353088}\cdot t^{18}-\frac{49775576589585}{1208925819614629174706176}\cdot t^{16}+\frac{5079140468325}{4835703278458516698824704}\cdot t^{14}-\frac{195434157555}{9671406556917033397649408}\cdot t^{12}+\frac{21714906395}{77371252455336267181195264}\cdot t^{10}-\frac{409715215}{154742504910672534362390528}\cdot t^8+\frac{9591995}{618970019642690137449562112}\cdot t^6-\frac{60025}{1237940039285380274899124224}\cdot t^4+\frac{2401}{39614081257132168796771975168}\cdot t^2-\frac{1}{79228162514264337593543950336}$

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.