Rule: Q[3, 12, 16, 90]

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.

• $P_1$:
  $4\cdot t^3-3\cdot t$
• $P_2$:
  $4\cdot t^{15}-15\cdot t^{13}+\frac{45}{2}\cdot t^{11}-\frac{275}{16}\cdot t^9+\frac{225}{32}\cdot t^7-\frac{189}{128}\cdot t^5+\frac{35}{256}\cdot t^3-\frac{15}{4096}\cdot t$
• $P_3$:
  $4\cdot t^{31}-32\cdot t^{29}+\frac{463}{4}\cdot t^{27}-\frac{1001}{4}\cdot t^{25}+\frac{11525}{32}\cdot t^{23}-\frac{5819}{16}\cdot t^{21}+\frac{270963}{1024}\cdot t^{19}-\frac{143583}{1024}\cdot t^{17}+\frac{442833}{8192}\cdot t^{15}-\frac{30685}{2048}\cdot t^{13}+\frac{382109}{131072}\cdot t^{11}-\frac{50167}{131072}\cdot t^9+\frac{33371}{1048576}\cdot t^7-\frac{791}{524288}\cdot t^5+\frac{2255}{67108864}\cdot t^3-\frac{15}{67108864}\cdot t$
• $P_4$:
  $4\cdot t^{121}-122\cdot t^{119}+\frac{3629}{2}\cdot t^{117}-\frac{70151}{4}\cdot t^{115}+\frac{1981795}{16}\cdot t^{113}-\frac{21807079}{32}\cdot t^{111}+\frac{389221833}{128}\cdot t^{109}-\frac{2895883551}{256}\cdot t^{107}+\frac{586438977663}{16384}\cdot t^{105}-\frac{3204720010635}{32768}\cdot t^{103}+\frac{30603768273975}{131072}\cdot t^{101}-\frac{128880494308605}{262144}\cdot t^{99}+\frac{482340302169635}{524288}\cdot t^{97}-\frac{1614282242385365}{1048576}\cdot t^{95}+\frac{9712635613875775}{4194304}\cdot t^{93}-\frac{26377727534962545}{8388608}\cdot t^{91}+\frac{2076959328948572565}{536870912}\cdot t^{89}-\frac{4644346064223755505}{1073741824}\cdot t^{87}+\frac{18923856021362172265}{4294967296}\cdot t^{85}-\frac{35200019455364238475}{8589934592}\cdot t^{83}+\frac{119769123509987101997}{34359738368}\cdot t^{81}-\frac{186627398670186546177}{68719476736}\cdot t^{79}+\frac{533320579386136664343}{274877906944}\cdot t^{77}-\frac{699363701301123909297}{549755813888}\cdot t^{75}+\frac{53901836188093738912275}{70368744177664}\cdot t^{73}-\frac{59635557563598111914559}{140737488355328}\cdot t^{71}+\frac{121255218957043674406323}{562949953421312}\cdot t^{69}-\frac{113271772351415041184961}{1125899906842624}\cdot t^{67}+\frac{24302141255266869613971}{562949953421312}\cdot t^{65}-\frac{38303496973894837215795}{2251799813685248}\cdot t^{63}+\frac{55404729117515649339633}{9007199254740992}\cdot t^{61}-\frac{36743976325269331111983}{18014398509481984}\cdot t^{59}+\frac{1428641970988219629741489}{2305843009213693952}\cdot t^{57}-\frac{794077718622481025045901}{4611686018427387904}\cdot t^{55}+\frac{806458444254358996914765}{18446744073709551616}\cdot t^{53}-\frac{373494435077747298677895}{36893488147419103232}\cdot t^{51}+\frac{314907072712610467512735}{147573952589676412928}\cdot t^{49}-\frac{120572925290771870748195}{295147905179352825856}\cdot t^{47}+\frac{83646525801137747023485}{1180591620717411303424}\cdot t^{45}-\frac{26210381190861779509675}{2361183241434822606848}\cdot t^{43}+\frac{236646965565453412821005}{151115727451828646838272}\cdot t^{41}-\frac{59902326323398723207505}{302231454903657293676544}\cdot t^{39}+\frac{27094917633505325556645}{1208925819614629174706176}\cdot t^{37}-\frac{5449325011811526437655}{2417851639229258349412352}\cdot t^{35}+\frac{969467439183376876575}{4835703278458516698824704}\cdot t^{33}-\frac{151646776665757488661}{9671406556917033397649408}\cdot t^{31}+\frac{41425368775966162127}{38685626227668133590597632}\cdot t^{29}-\frac{4901302339200697409}{77371252455336267181195264}\cdot t^{27}+\frac{15927024196385019627}{4951760157141521099596496896}\cdot t^{25}-\frac{1373223551914438575}{9903520314283042199192993792}\cdot t^{23}+\frac{198501359253020967}{39614081257132168796771975168}\cdot t^{21}-\frac{11844132949743237}{79228162514264337593543950336}\cdot t^{19}+\frac{1145399201036343}{316912650057057350374175801344}\cdot t^{17}-\frac{43861638984867}{633825300114114700748351602688}\cdot t^{15}+\frac{2584081406165}{2535301200456458802993406410752}\cdot t^{13}-\frac{56372133923}{5070602400912917605986812821504}\cdot t^{11}+\frac{110715608719}{1298074214633706907132624082305024}\cdot t^9-\frac{1109776843}{2596148429267413814265248164610048}\cdot t^7+\frac{12959999}{10384593717069655257060992658440192}\cdot t^5-\frac{36005}{20769187434139310514121985316880384}\cdot t^3+\frac{15}{20769187434139310514121985316880384}\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.