Rule: Q[2, 20, 44, 67]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{22}-11\cdot t^{20}+\frac{209}{8}\cdot t^{18}-\frac{561}{16}\cdot t^{16}+\frac{935}{32}\cdot t^{14}-\frac{1001}{64}\cdot t^{12}+\frac{11011}{2048}\cdot t^{10}-\frac{4719}{4096}\cdot t^8+\frac{4719}{32768}\cdot t^6-\frac{605}{65536}\cdot t^4+\frac{121}{524288}\cdot t^2-\frac{1}{1048576}$
• $P_3$:
  $2\cdot t^{66}-33\cdot t^{64}+\frac{2079}{8}\cdot t^{62}-\frac{20801}{16}\cdot t^{60}+\frac{593835}{128}\cdot t^{58}-\frac{3218391}{256}\cdot t^{56}+\frac{27535123}{1024}\cdot t^{54}-\frac{95406201}{2048}\cdot t^{52}+\frac{2181183147}{32768}\cdot t^{50}-\frac{5208478275}{65536}\cdot t^{48}+\frac{20982726765}{262144}\cdot t^{46}-\frac{35896069755}{524288}\cdot t^{44}+\frac{209615320915}{4194304}\cdot t^{42}-\frac{261943093335}{8388608}\cdot t^{40}+\frac{561306628575}{33554432}\cdot t^{38}-\frac{515815110965}{67108864}\cdot t^{36}+\frac{6499270398159}{2147483648}\cdot t^{34}-\frac{4377059655903}{4294967296}\cdot t^{32}+\frac{5025512938259}{17179869184}\cdot t^{30}-\frac{2448038217405}{34359738368}\cdot t^{28}+\frac{4023297592083}{274877906944}\cdot t^{26}-\frac{1383673775055}{549755813888}\cdot t^{24}+\frac{789037111395}{2199023255552}\cdot t^{22}-\frac{184294815705}{4398046511104}\cdot t^{20}+\frac{277904880825}{70368744177664}\cdot t^{18}-\frac{41482387089}{140737488355328}\cdot t^{16}+\frac{9572858559}{562949953421312}\cdot t^{14}-\frac{827284073}{1125899906842624}\cdot t^{12}+\frac{205265973}{9007199254740992}\cdot t^{10}-\frac{8608545}{18014398509481984}\cdot t^8+\frac{446369}{72057594037927936}\cdot t^6-\frac{6171}{144115188075855872}\cdot t^4+\frac{1089}{9223372036854775808}\cdot t^2-\frac{1}{18446744073709551616}$
• $P_4$:
  $2\cdot t^{133}-67\cdot t^{131}+1097\cdot t^{129}-11700\cdot t^{127}+\frac{11700129}{128}\cdot t^{125}-\frac{142780575}{256}\cdot t^{123}+\frac{1416879025}{512}\cdot t^{121}-\frac{11754707503}{1024}\cdot t^{119}+\frac{1330974064255}{32768}\cdot t^{117}-\frac{8158048894853}{65536}\cdot t^{115}+\frac{2739237305519}{8192}\cdot t^{113}-\frac{104173804476469}{131072}\cdot t^{111}+\frac{7065650374635489}{4194304}\cdot t^{109}-\frac{26880202856045655}{8388608}\cdot t^{107}+\frac{92264067050473719}{16777216}\cdot t^{105}-\frac{287011011559567341}{33554432}\cdot t^{103}+\frac{25991324040136884819}{2147483648}\cdot t^{101}-\frac{67131051785113595145}{4294967296}\cdot t^{99}+\frac{79341023753262503925}{4294967296}\cdot t^{97}-\frac{86019943245839238405}{4294967296}\cdot t^{95}+\frac{5486217099242612697195}{274877906944}\cdot t^{93}-\frac{10067506182232848729765}{549755813888}\cdot t^{91}+\frac{17033772722979973619295}{1099511627776}\cdot t^{89}-\frac{26604162689960333266425}{2199023255552}\cdot t^{87}+\frac{614288917897343758054895}{70368744177664}\cdot t^{85}-\frac{819723708985540652983781}{140737488355328}\cdot t^{83}+\frac{253011709786212013833413}{70368744177664}\cdot t^{81}-\frac{578246401760026464626847}{281474976710656}\cdot t^{79}+\frac{9787766913576039318118125}{9007199254740992}\cdot t^{77}-\frac{9586787063899427926771227}{18014398509481984}\cdot t^{75}+\frac{8692906331296997622208935}{36028797018963968}\cdot t^{73}-\frac{7295543401284385914789045}{72057594037927936}\cdot t^{71}+\frac{362547054144892190325143007}{9223372036854775808}\cdot t^{69}-\frac{260311643869911123357099645}{18446744073709551616}\cdot t^{67}+\frac{86357027304072397900581051}{18446744073709551616}\cdot t^{65}-\frac{13225484124241645756140147}{9223372036854775808}\cdot t^{63}+\frac{478266966725077993488856701}{1180591620717411303424}\cdot t^{61}-\frac{248969681778336310611402531}{2361183241434822606848}\cdot t^{59}+\frac{119243670535564469125575045}{4722366482869645213696}\cdot t^{57}-\frac{52465156670421730282438251}{9444732965739290427392}\cdot t^{55}+\frac{338703662439949572692029719}{302231454903657293676544}\cdot t^{53}-\frac{125081809863367014099451053}{604462909807314587353088}\cdot t^{51}+\frac{5273183010912233435576415}{151115727451828646838272}\cdot t^{49}-\frac{6480850137730467999001425}{1208925819614629174706176}\cdot t^{47}+\frac{28946268434802460894493985}{38685626227668133590597632}\cdot t^{45}-\frac{7318907966100057644738295}{77371252455336267181195264}\cdot t^{43}+\frac{1670428996907905259947215}{154742504910672534362390528}\cdot t^{41}-\frac{342827262004738948083045}{309485009821345068724781056}\cdot t^{39}+\frac{2015919884084184545328225}{19807040628566084398385987584}\cdot t^{37}-\frac{330083317180688080404915}{39614081257132168796771975168}\cdot t^{35}+\frac{23948423665578742454163}{39614081257132168796771975168}\cdot t^{33}-\frac{1530297620010132775373}{39614081257132168796771975168}\cdot t^{31}+\frac{5473129650665851026457}{2535301200456458802993406410752}\cdot t^{29}-\frac{530651059584748153975}{5070602400912917605986812821504}\cdot t^{27}+\frac{44215853331588757357}{10141204801825835211973625643008}\cdot t^{25}-\frac{3131814760173447595}{20282409603651670423947251286016}\cdot t^{23}+\frac{2978414661082188265}{649037107316853453566312041152512}\cdot t^{21}-\frac{146291314011420483}{1298074214633706907132624082305024}\cdot t^{19}+\frac{1456951668150945}{649037107316853453566312041152512}\cdot t^{17}-\frac{92000326802469}{2596148429267413814265248164610048}\cdot t^{15}+\frac{35773801426307}{83076749736557242056487941267521536}\cdot t^{13}-\frac{644201441429}{166153499473114484112975882535043072}\cdot t^{11}+\frac{8162906609}{332306998946228968225951765070086144}\cdot t^9-\frac{67593955}{664613997892457936451903530140172288}\cdot t^7+\frac{41744417}{170141183460469231731687303715884105728}\cdot t^5-\frac{95843}{340282366920938463463374607431768211456}\cdot t^3+\frac{33}{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.