Rule: Q[1, 42, 86]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{43}-\frac{43}{4}\cdot t^{41}+\frac{215}{4}\cdot t^{39}-\frac{10621}{64}\cdot t^{37}+\frac{90687}{256}\cdot t^{35}-\frac{567987}{1024}\cdot t^{33}+\frac{168861}{256}\cdot t^{31}-\frac{1246355}{2048}\cdot t^{29}+\frac{7228859}{16384}\cdot t^{27}-\frac{16583853}{65536}\cdot t^{25}+\frac{7538115}{65536}\cdot t^{23}-\frac{173376645}{4194304}\cdot t^{21}+\frac{195747825}{16777216}\cdot t^{19}-\frac{171655785}{67108864}\cdot t^{17}+\frac{14375115}{33554432}\cdot t^{15}-\frac{14375115}{268435456}\cdot t^{13}+\frac{20764055}{4294967296}\cdot t^{11}-\frac{5167525}{17179869184}\cdot t^9+\frac{206701}{17179869184}\cdot t^7-\frac{76153}{274877906944}\cdot t^5+\frac{3311}{1099511627776}\cdot t^3-\frac{43}{4398046511104}\cdot t$
• $P_3$:
  $t^{129}-\frac{129}{4}\cdot t^{127}+\frac{8127}{16}\cdot t^{125}-\frac{166625}{32}\cdot t^{123}+\frac{10001499}{256}\cdot t^{121}-\frac{117114327}{512}\cdot t^{119}+\frac{2228346043}{2048}\cdot t^{117}-\frac{17706740337}{4096}\cdot t^{115}+\frac{959237048835}{65536}\cdot t^{113}-\frac{5620418560211}{131072}\cdot t^{111}+\frac{57668328252249}{524288}\cdot t^{109}-\frac{261506764324143}{1048576}\cdot t^{107}+\frac{4225085072598903}{8388608}\cdot t^{105}-\frac{15297721814582235}{16777216}\cdot t^{103}+\frac{99824761108075131}{67108864}\cdot t^{101}-\frac{294804119061859305}{134217728}\cdot t^{99}+\frac{12655706031584774235}{4294967296}\cdot t^{97}-\frac{30947987018413187415}{8589934592}\cdot t^{95}+\frac{138321083120335217025}{34359738368}\cdot t^{93}-\frac{283128035209949310255}{68719476736}\cdot t^{91}+\frac{2127356521439894358705}{549755813888}\cdot t^{89}-\frac{3673160554655478972085}{1099511627776}\cdot t^{87}+\frac{11674845909062146843305}{4398046511104}\cdot t^{85}-\frac{17095652130989279832075}{8796093022208}\cdot t^{83}+\frac{184687314926211172281115}{140737488355328}\cdot t^{81}-\frac{230148807831124691611851}{281474976710656}\cdot t^{79}+\frac{529565703456083028271929}{1125899906842624}\cdot t^{77}-\frac{562639523715504335774751}{2251799813685248}\cdot t^{75}+\frac{2208380025898903156683075}{18014398509481984}\cdot t^{73}-\frac{2001249209676661205435559}{36028797018963968}\cdot t^{71}+\frac{3348891775115490300004959}{144115188075855872}\cdot t^{69}-\frac{2586076400401889481175653}{288230376151711744}\cdot t^{67}+\frac{58946545580294614875045039}{18446744073709551616}\cdot t^{65}-\frac{38702277401203535018968965}{36893488147419103232}\cdot t^{63}+\frac{46802196758235606125106123}{147573952589676412928}\cdot t^{61}-\frac{26032832847286066628858421}{295147905179352825856}\cdot t^{59}+\frac{53216459978143918759828863}{2361183241434822606848}\cdot t^{57}-\frac{24951078180116831474937387}{4722366482869645213696}\cdot t^{55}+\frac{21429931230464716448977455}{18889465931478580854784}\cdot t^{53}-\frac{8413232260849110902191149}{37778931862957161709568}\cdot t^{51}+\frac{24105328387826104270322955}{604462909807314587353088}\cdot t^{49}-\frac{7856947390267045072588635}{1208925819614629174706176}\cdot t^{47}+\frac{4648801384170046920343905}{4835703278458516698824704}\cdot t^{45}-\frac{1244541203441954151200775}{9671406556917033397649408}\cdot t^{43}+\frac{1201947279901694757790695}{77371252455336267181195264}\cdot t^{41}-\frac{260739886116240661742955}{154742504910672534362390528}\cdot t^{39}+\frac{101209143851301377868795}{618970019642690137449562112}\cdot t^{37}-\frac{17489696368699200223305}{1237940039285380274899124224}\cdot t^{35}+\frac{42824565182617383262825}{39614081257132168796771975168}\cdot t^{33}-\frac{5768206738883157745605}{79228162514264337593543950336}\cdot t^{31}+\frac{1358084118268692836307}{316912650057057350374175801344}\cdot t^{29}-\frac{138607881351706709789}{633825300114114700748351602688}\cdot t^{27}+\frac{48602763590858196939}{5070602400912917605986812821504}\cdot t^{25}-\frac{3619868191970570775}{10141204801825835211973625643008}\cdot t^{23}+\frac{452260075342496003}{40564819207303340847894502572032}\cdot t^{21}-\frac{23335286442733209}{81129638414606681695789005144064}\cdot t^{19}+\frac{7808872762636749}{1298074214633706907132624082305024}\cdot t^{17}-\frac{258773561334941}{2596148429267413814265248164610048}\cdot t^{15}+\frac{13196320514895}{10384593717069655257060992658440192}\cdot t^{13}-\frac{249228329337}{20769187434139310514121985316880384}\cdot t^{11}+\frac{13244017501}{166153499473114484112975882535043072}\cdot t^9-\frac{114943257}{332306998946228968225951765070086144}\cdot t^7+\frac{1162161}{1329227995784915872903807060280344576}\cdot t^5-\frac{2795}{2658455991569831745807614120560689152}\cdot t^3+\frac{129}{340282366920938463463374607431768211456}\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.