Rule: Q[1, 16, 18, 34, 68]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{17}-\frac{17}{4}\cdot t^{15}+\frac{119}{16}\cdot t^{13}-\frac{221}{32}\cdot t^{11}+\frac{935}{256}\cdot t^9-\frac{561}{512}\cdot t^7+\frac{357}{2048}\cdot t^5-\frac{51}{4096}\cdot t^3+\frac{17}{65536}\cdot t$
• $P_3$:
  $t^{35}-9\cdot t^{33}+\frac{593}{16}\cdot t^{31}-\frac{185}{2}\cdot t^{29}+\frac{39991}{256}\cdot t^{27}-\frac{48321}{256}\cdot t^{25}+\frac{344565}{2048}\cdot t^{23}-\frac{115115}{1024}\cdot t^{21}+\frac{3712775}{65536}\cdot t^{19}-\frac{1408451}{65536}\cdot t^{17}+\frac{3187041}{524288}\cdot t^{15}-\frac{165053}{131072}\cdot t^{13}+\frac{1557829}{8388608}\cdot t^{11}-\frac{156655}{8388608}\cdot t^9+\frac{80427}{67108864}\cdot t^7-\frac{1479}{33554432}\cdot t^5+\frac{3281}{4294967296}\cdot t^3-\frac{17}{4294967296}\cdot t$
• $P_4$:
  $t^{69}-\frac{35}{2}\cdot t^{67}+\frac{293}{2}\cdot t^{65}-781\cdot t^{63}+\frac{762321}{256}\cdot t^{61}-\frac{4426831}{512}\cdot t^{59}+\frac{20352345}{1024}\cdot t^{57}-\frac{76038551}{2048}\cdot t^{55}+\frac{3762299079}{65536}\cdot t^{53}-\frac{9759379773}{131072}\cdot t^{51}+\frac{2680578615}{32768}\cdot t^{49}-\frac{20102143425}{262144}\cdot t^{47}+\frac{517169301285}{8388608}\cdot t^{45}-\frac{715773766995}{16777216}\cdot t^{43}+\frac{854585539115}{33554432}\cdot t^{41}-\frac{881081313945}{67108864}\cdot t^{39}+\frac{25100044895975}{4294967296}\cdot t^{37}-\frac{19272728236965}{8589934592}\cdot t^{35}+\frac{6367972006277}{8589934592}\cdot t^{33}-\frac{1804965057467}{8589934592}\cdot t^{31}+\frac{27964935632513}{549755813888}\cdot t^{29}-\frac{11498361324175}{1099511627776}\cdot t^{27}+\frac{3986352710613}{2199023255552}\cdot t^{25}-\frac{1154967365955}{4398046511104}\cdot t^{23}+\frac{4425469016085}{140737488355328}\cdot t^{21}-\frac{864137913639}{281474976710656}\cdot t^{19}+\frac{33814999485}{140737488355328}\cdot t^{17}-\frac{8305072577}{562949953421312}\cdot t^{15}+\frac{12452236891}{18014398509481984}\cdot t^{13}-\frac{858404477}{36028797018963968}\cdot t^{11}+\frac{41396377}{72057594037927936}\cdot t^9-\frac{1298715}{144115188075855872}\cdot t^7+\frac{1514513}{18446744073709551616}\cdot t^5-\frac{13107}{36893488147419103232}\cdot t^3+\frac{17}{36893488147419103232}\cdot t$
• $P_5$:
  $t^{137}-\frac{69}{2}\cdot t^{135}+\frac{4657}{8}\cdot t^{133}-\frac{102443}{16}\cdot t^{131}+\frac{825955}{16}\cdot t^{129}-\frac{5204849}{16}\cdot t^{127}+\frac{106768011}{64}\cdot t^{125}-\frac{916238325}{128}\cdot t^{123}+\frac{1718449417425}{65536}\cdot t^{121}-\frac{10913912882125}{131072}\cdot t^{119}+\frac{121616427182525}{524288}\cdot t^{117}-\frac{600145739138231}{1048576}\cdot t^{115}+\frac{5287006104036371}{4194304}\cdot t^{113}-\frac{20920937295078359}{8388608}\cdot t^{111}+\frac{149541678023632345}{33554432}\cdot t^{109}-\frac{484907819165929359}{67108864}\cdot t^{107}+\frac{45826943079878264295}{4294967296}\cdot t^{105}-\frac{123671875613288173587}{8589934592}\cdot t^{103}+\frac{611655838438696971231}{34359738368}\cdot t^{101}-\frac{1389352126394875113525}{68719476736}\cdot t^{99}+\frac{2904750960040676273835}{137438953472}\cdot t^{97}-\frac{5599613082684757141005}{274877906944}\cdot t^{95}+\frac{19935871253298370293735}{1099511627776}\cdot t^{93}-\frac{32811266179516070369865}{2199023255552}\cdot t^{91}+\frac{1599377102155179935057925}{140737488355328}\cdot t^{89}-\frac{2256751961830217599068321}{281474976710656}\cdot t^{87}+\frac{5903217072144528249692313}{1125899906842624}\cdot t^{85}-\frac{7160114316902648959351067}{2251799813685248}\cdot t^{83}+\frac{16113257891485285507787741}{9007199254740992}\cdot t^{81}-\frac{16822860027230644744863345}{18014398509481984}\cdot t^{79}+\frac{32594748862705443155988519}{72057594037927936}\cdot t^{77}-\frac{29297070547526042579070753}{144115188075855872}\cdot t^{75}+\frac{1563281053442210736027624615}{18446744073709551616}\cdot t^{73}-\frac{1208549601106967716572707235}{36893488147419103232}\cdot t^{71}+\frac{1731789064427220818492811975}{147573952589676412928}\cdot t^{69}-\frac{1149176645040421025468800605}{295147905179352825856}\cdot t^{67}+\frac{176427485791394020596521031}{147573952589676412928}\cdot t^{65}-\frac{200343776333309671952484231}{590295810358705651712}\cdot t^{63}+\frac{210112367222981779962623373}{2361183241434822606848}\cdot t^{61}-\frac{101629444697298581993874195}{4722366482869645213696}\cdot t^{59}+\frac{2897820598145546975117904321}{604462909807314587353088}\cdot t^{57}-\frac{1187271652002648139081374045}{1208925819614629174706176}\cdot t^{55}+\frac{893063987716254700875990813}{4835703278458516698824704}\cdot t^{53}-\frac{307704295317195686704870647}{9671406556917033397649408}\cdot t^{51}+\frac{193814559502556402278004175}{38685626227668133590597632}\cdot t^{49}-\frac{55653562832846188529614995}{77371252455336267181195264}\cdot t^{47}+\frac{29060392371244568943141645}{309485009821345068724781056}\cdot t^{45}-\frac{6877046356797218990583195}{618970019642690137449562112}\cdot t^{43}+\frac{47040173393407605770511285}{39614081257132168796771975168}\cdot t^{41}-\frac{9047332919004986038131225}{79228162514264337593543950336}\cdot t^{39}+\frac{3117837329216582404999437}{316912650057057350374175801344}\cdot t^{37}-\frac{478951687334993594775183}{633825300114114700748351602688}\cdot t^{35}+\frac{65234774633488894701207}{1267650600228229401496703205376}\cdot t^{33}-\frac{7829107288550134389693}{2535301200456458802993406410752}\cdot t^{31}+\frac{1644147186173194580295}{10141204801825835211973625643008}\cdot t^{29}-\frac{149820805017639184457}{20282409603651670423947251286016}\cdot t^{27}+\frac{375581601583161287483}{1298074214633706907132624082305024}\cdot t^{25}-\frac{25019389874414108095}{2596148429267413814265248164610048}\cdot t^{23}+\frac{2798064539909668535}{10384593717069655257060992658440192}\cdot t^{21}-\frac{129326454907663925}{20769187434139310514121985316880384}\cdot t^{19}+\frac{9698436318126855}{83076749736557242056487941267521536}\cdot t^{17}-\frac{288272095840947}{166153499473114484112975882535043072}\cdot t^{15}+\frac{13193243048517}{664613997892457936451903530140172288}\cdot t^{13}-\frac{223735976243}{1329227995784915872903807060280344576}\cdot t^{11}+\frac{341781911185}{340282366920938463463374607431768211456}\cdot t^9-\frac{2665832917}{680564733841876926926749214863536422912}\cdot t^7+\frac{24232225}{2722258935367507707706996859454145691648}\cdot t^5-\frac{52411}{5444517870735015415413993718908291383296}\cdot t^3+\frac{17}{5444517870735015415413993718908291383296}\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.