Rule: Q[1, 32, 34, 66]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{33}-\frac{33}{4}\cdot t^{31}+\frac{495}{16}\cdot t^{29}-\frac{2233}{32}\cdot t^{27}+\frac{27027}{256}\cdot t^{25}-\frac{57915}{512}\cdot t^{23}+\frac{180895}{2048}\cdot t^{21}-\frac{208725}{4096}\cdot t^{19}+\frac{1427679}{65536}\cdot t^{17}-\frac{898909}{131072}\cdot t^{15}+\frac{820743}{524288}\cdot t^{13}-\frac{264537}{1048576}\cdot t^{11}+\frac{230945}{8388608}\cdot t^9-\frac{31977}{16777216}\cdot t^7+\frac{5049}{67108864}\cdot t^5-\frac{187}{134217728}\cdot t^3+\frac{33}{4294967296}\cdot t$
• $P_3$:
  $t^{67}-17\cdot t^{65}+\frac{2209}{16}\cdot t^{63}-713\cdot t^{61}+\frac{673135}{256}\cdot t^{59}-\frac{1887233}{256}\cdot t^{57}+\frac{33451761}{2048}\cdot t^{55}-\frac{30056499}{1024}\cdot t^{53}+\frac{2855107827}{65536}\cdot t^{51}-\frac{3546403575}{65536}\cdot t^{49}+\frac{29776261515}{524288}\cdot t^{47}-\frac{6647420325}{131072}\cdot t^{45}+\frac{324837273215}{8388608}\cdot t^{43}-\frac{212768262805}{8388608}\cdot t^{41}+\frac{958190103325}{67108864}\cdot t^{39}-\frac{231926696085}{33554432}\cdot t^{37}+\frac{12351427293471}{4294967296}\cdot t^{35}-\frac{4409214364119}{4294967296}\cdot t^{33}+\frac{10773167031869}{34359738368}\cdot t^{31}-\frac{350450612105}{4294967296}\cdot t^{29}+\frac{9893428758983}{549755813888}\cdot t^{27}-\frac{1836512465073}{549755813888}\cdot t^{25}+\frac{2275628770545}{4398046511104}\cdot t^{23}-\frac{145467913695}{2199023255552}\cdot t^{21}+\frac{969342861825}{140737488355328}\cdot t^{19}-\frac{80820408357}{140737488355328}\cdot t^{17}+\frac{42255951417}{1125899906842624}\cdot t^{15}-\frac{526453501}{281474976710656}\cdot t^{13}+\frac{1234423193}{18014398509481984}\cdot t^{11}-\frac{31622635}{18014398509481984}\cdot t^9+\frac{4214419}{144115188075855872}\cdot t^7-\frac{20383}{72057594037927936}\cdot t^5+\frac{23969}{18446744073709551616}\cdot t^3-\frac{33}{18446744073709551616}\cdot t$
• $P_4$:
  $t^{133}-\frac{67}{2}\cdot t^{131}+\frac{1097}{2}\cdot t^{129}-5850\cdot t^{127}+\frac{11700129}{256}\cdot t^{125}-\frac{142780575}{512}\cdot t^{123}+\frac{1416879025}{1024}\cdot t^{121}-\frac{11754707503}{2048}\cdot t^{119}+\frac{1330974064255}{65536}\cdot t^{117}-\frac{8158048894853}{131072}\cdot t^{115}+\frac{2739237305519}{16384}\cdot t^{113}-\frac{104173804476469}{262144}\cdot t^{111}+\frac{7065650374635489}{8388608}\cdot t^{109}-\frac{26880202856045655}{16777216}\cdot t^{107}+\frac{92264067050473719}{33554432}\cdot t^{105}-\frac{287011011559567341}{67108864}\cdot t^{103}+\frac{25991324040136884819}{4294967296}\cdot t^{101}-\frac{67131051785113595145}{8589934592}\cdot t^{99}+\frac{79341023753262503925}{8589934592}\cdot t^{97}-\frac{86019943245839238405}{8589934592}\cdot t^{95}+\frac{5486217099242612697195}{549755813888}\cdot t^{93}-\frac{10067506182232848729765}{1099511627776}\cdot t^{91}+\frac{17033772722979973619295}{2199023255552}\cdot t^{89}-\frac{26604162689960333266425}{4398046511104}\cdot t^{87}+\frac{614288917897343758054895}{140737488355328}\cdot t^{85}-\frac{819723708985540652983781}{281474976710656}\cdot t^{83}+\frac{253011709786212013833413}{140737488355328}\cdot t^{81}-\frac{578246401760026464626847}{562949953421312}\cdot t^{79}+\frac{9787766913576039318118125}{18014398509481984}\cdot t^{77}-\frac{9586787063899427926771227}{36028797018963968}\cdot t^{75}+\frac{8692906331296997622208935}{72057594037927936}\cdot t^{73}-\frac{7295543401284385914789045}{144115188075855872}\cdot t^{71}+\frac{362547054144892190325143007}{18446744073709551616}\cdot t^{69}-\frac{260311643869911123357099645}{36893488147419103232}\cdot t^{67}+\frac{86357027304072397900581051}{36893488147419103232}\cdot t^{65}-\frac{13225484124241645756140147}{18446744073709551616}\cdot t^{63}+\frac{478266966725077993488856701}{2361183241434822606848}\cdot t^{61}-\frac{248969681778336310611402531}{4722366482869645213696}\cdot t^{59}+\frac{119243670535564469125575045}{9444732965739290427392}\cdot t^{57}-\frac{52465156670421730282438251}{18889465931478580854784}\cdot t^{55}+\frac{338703662439949572692029719}{604462909807314587353088}\cdot t^{53}-\frac{125081809863367014099451053}{1208925819614629174706176}\cdot t^{51}+\frac{5273183010912233435576415}{302231454903657293676544}\cdot t^{49}-\frac{6480850137730467999001425}{2417851639229258349412352}\cdot t^{47}+\frac{28946268434802460894493985}{77371252455336267181195264}\cdot t^{45}-\frac{7318907966100057644738295}{154742504910672534362390528}\cdot t^{43}+\frac{1670428996907905259947215}{309485009821345068724781056}\cdot t^{41}-\frac{342827262004738948083045}{618970019642690137449562112}\cdot t^{39}+\frac{2015919884084184545328225}{39614081257132168796771975168}\cdot t^{37}-\frac{330083317180688080404915}{79228162514264337593543950336}\cdot t^{35}+\frac{23948423665578742454163}{79228162514264337593543950336}\cdot t^{33}-\frac{1530297620010132775373}{79228162514264337593543950336}\cdot t^{31}+\frac{5473129650665851026457}{5070602400912917605986812821504}\cdot t^{29}-\frac{530651059584748153975}{10141204801825835211973625643008}\cdot t^{27}+\frac{44215853331588757357}{20282409603651670423947251286016}\cdot t^{25}-\frac{3131814760173447595}{40564819207303340847894502572032}\cdot t^{23}+\frac{2978414661082188265}{1298074214633706907132624082305024}\cdot t^{21}-\frac{146291314011420483}{2596148429267413814265248164610048}\cdot t^{19}+\frac{1456951668150945}{1298074214633706907132624082305024}\cdot t^{17}-\frac{92000326802469}{5192296858534827628530496329220096}\cdot t^{15}+\frac{35773801426307}{166153499473114484112975882535043072}\cdot t^{13}-\frac{644201441429}{332306998946228968225951765070086144}\cdot t^{11}+\frac{8162906609}{664613997892457936451903530140172288}\cdot t^9-\frac{67593955}{1329227995784915872903807060280344576}\cdot t^7+\frac{41744417}{340282366920938463463374607431768211456}\cdot t^5-\frac{95843}{680564733841876926926749214863536422912}\cdot t^3+\frac{33}{680564733841876926926749214863536422912}\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.